{"id":261432,"date":"2024-06-25T22:45:42","date_gmt":"2024-06-25T22:45:42","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=261432"},"modified":"2024-06-25T22:45:42","modified_gmt":"2024-06-25T22:45:42","slug":"what-do-you-expect-probability-and-expected-value-investigation-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/","title":{"rendered":"What do you expect probability and expected value Investigation 2?"},"content":{"rendered":"<p>Probability and expected value are essential concepts in the field of statistics. Investigation 2 focuses on these concepts and aims to provide a deeper understanding of their applications. By exploring various scenarios and conducting experiments, students can gain valuable insights into how probability and expected value play a crucial role in decision making and prediction. Let&#8217;s delve into the details of Investigation 2 and explore its key components.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#1_Understanding_Probability_and_Expected_Value\" title=\"1. Understanding Probability and Expected Value:\">1. Understanding Probability and Expected Value:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#2_Investigating_Real-Life_Scenarios\" title=\"2. Investigating Real-Life Scenarios:\">2. Investigating Real-Life Scenarios:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#3_Conducting_Experiments\" title=\"3. Conducting Experiments:\">3. Conducting Experiments:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#4_Investigating_Dice_Rolling\" title=\"4. Investigating Dice Rolling:\">4. Investigating Dice Rolling:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#5_Calculating_Expected_Value\" title=\"5. Calculating Expected Value:\">5. Calculating Expected Value:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#6_Discussing_Probability_Distributions\" title=\"6. Discussing Probability Distributions:\">6. Discussing Probability Distributions:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#7_Analyzing_Gamble_Situations\" title=\"7. Analyzing Gamble Situations:\">7. Analyzing Gamble Situations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#8_Exploring_Complex_Probability_Situations\" title=\"8. Exploring Complex Probability Situations:\">8. Exploring Complex Probability Situations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#9_Building_Decision-Making_Skills\" title=\"9. Building Decision-Making Skills:\">9. Building Decision-Making Skills:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#10_Applying_Probability_in_Real_Life\" title=\"10. Applying Probability in Real Life:\">10. Applying Probability in Real Life:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#11_Gaining_a_Foundation_for_Further_Statistical_Concepts\" title=\"11. Gaining a Foundation for Further Statistical Concepts:\">11. Gaining a Foundation for Further Statistical Concepts:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#12_Enhancing_Critical_Thinking_Skills\" title=\"12. Enhancing Critical Thinking Skills:\">12. Enhancing Critical Thinking Skills:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#FAQs\" title=\"FAQs:\">FAQs:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#1_What_is_the_difference_between_probability_and_expected_value\" title=\"1. What is the difference between probability and expected value?\">1. What is the difference between probability and expected value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#2_How_are_probability_and_expected_value_calculated\" title=\"2. How are probability and expected value calculated?\">2. How are probability and expected value calculated?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#3_How_are_probability_and_expected_value_used_in_decision_making\" title=\"3. How are probability and expected value used in decision making?\">3. How are probability and expected value used in decision making?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#4_Can_probability_and_expected_value_be_applied_in_real-life_situations\" title=\"4. Can probability and expected value be applied in real-life situations?\">4. Can probability and expected value be applied in real-life situations?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#5_How_does_Investigation_2_contribute_to_statistical_understanding\" title=\"5. How does Investigation 2 contribute to statistical understanding?\">5. How does Investigation 2 contribute to statistical understanding?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#6_How_do_probability_distributions_relate_to_Investigation_2\" title=\"6. How do probability distributions relate to Investigation 2?\">6. How do probability distributions relate to Investigation 2?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#7_Can_expected_value_be_negative\" title=\"7. Can expected value be negative?\">7. Can expected value be negative?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#8_What_are_some_other_applications_of_probability_and_expected_value\" title=\"8. What are some other applications of probability and expected value?\">8. What are some other applications of probability and expected value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#9_How_does_Investigation_2_enhance_critical_thinking_skills\" title=\"9. How does Investigation 2 enhance critical thinking skills?\">9. How does Investigation 2 enhance critical thinking skills?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#10_What_is_the_significance_of_gamble_situations_in_Investigation_2\" title=\"10. What is the significance of gamble situations in Investigation 2?\">10. What is the significance of gamble situations in Investigation 2?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#11_Can_probability_and_expected_value_be_used_to_predict_events_accurately\" title=\"11. Can probability and expected value be used to predict events accurately?\">11. Can probability and expected value be used to predict events accurately?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#12_How_can_probability_and_expected_value_improve_our_daily_lives\" title=\"12. How can probability and expected value improve our daily lives?\">12. How can probability and expected value improve our daily lives?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"1_Understanding_Probability_and_Expected_Value\"><\/span>1. Understanding Probability and Expected Value:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Probability refers to the likelihood or chance of an event occurring. It is expressed as a value between 0 and 1, where 0 indicates an impossible event, and 1 represents a certain event. Expected value, on the other hand, is the average value or outcome that one can anticipate based on the probabilities and associated values.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"2_Investigating_Real-Life_Scenarios\"><\/span>2. Investigating Real-Life Scenarios:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Investigation 2 involves examining real-life scenarios and determining the probabilities associated with certain outcomes. By doing so, students develop their skills in applying probability to practical situations, such as determining the chances of winning a game or predicting the outcome of an experiment.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"3_Conducting_Experiments\"><\/span>3. Conducting Experiments:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To understand probability and expected value better, students perform experiments where they collect data and analyze the results. By conducting multiple trials, they can observe the outcomes and calculate the relative frequencies of each event. This process helps students grasp the connection between experimental outcomes and theoretical probabilities.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"4_Investigating_Dice_Rolling\"><\/span>4. Investigating Dice Rolling:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>One of the primary topics explored in Investigation 2 is dice rolling. Students investigate the probabilities associated with rolling dice and analyze the expected values related to different outcomes. This exercise provides them with a concrete example to understand the concepts of probability and expected value.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"5_Calculating_Expected_Value\"><\/span>5. Calculating Expected Value:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Expected value is calculated by multiplying each possible outcome by its respective probability and summing up these values. By performing these calculations, students gain insights into the average outcome they can expect from a given experiment or scenario.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"6_Discussing_Probability_Distributions\"><\/span>6. Discussing Probability Distributions:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Probability distributions represent the various possible outcomes of an event along with their associated probabilities. In Investigation 2, students explore the concept of probability distributions to better understand the set of possible outcomes and their likelihoods.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"7_Analyzing_Gamble_Situations\"><\/span>7. Analyzing Gamble Situations:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Investigation 2 also involves analyzing gamble situations. By examining different games of chance, students can determine the expected value and make decisions based on the potential outcomes and associated probabilities.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"8_Exploring_Complex_Probability_Situations\"><\/span>8. Exploring Complex Probability Situations:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Students are exposed to more complex probability situations, such as flipping multiple coins or rolling multiple dice. By exploring these scenarios, they develop their ability to handle calculations involving multiple events and gain a deeper understanding of the principles behind probability.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"9_Building_Decision-Making_Skills\"><\/span>9. Building Decision-Making Skills:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>By considering the expected values and probabilities associated with different outcomes, students enhance their decision-making skills. They learn to evaluate the risks and rewards of various scenarios before making informed choices.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"10_Applying_Probability_in_Real_Life\"><\/span>10. Applying Probability in Real Life:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Investigation 2 emphasizes the practical applications of probability in real-life situations, such as predicting the likelihood of an event occurring, determining insurance rates, or making investment decisions. By understanding probability and expected value, students can make more informed choices in their daily lives.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"11_Gaining_a_Foundation_for_Further_Statistical_Concepts\"><\/span>11. Gaining a Foundation for Further Statistical Concepts:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Investigation 2 serves as a stepping stone for students to explore more advanced statistical concepts. By grasping the fundamentals of probability and expected value, they build a strong foundation for future investigations and statistical analysis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"12_Enhancing_Critical_Thinking_Skills\"><\/span>12. Enhancing Critical Thinking Skills:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Through Investigation 2, students develop critical thinking skills by analyzing data, making predictions, and evaluating the likelihood of outcomes. This process helps them approach problems from a logical and analytical perspective.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_the_difference_between_probability_and_expected_value\"><\/span>1. What is the difference between probability and expected value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nProbability refers to the likelihood or chance of an event occurring, while expected value represents the average outcome based on probabilities and associated values.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_How_are_probability_and_expected_value_calculated\"><\/span>2. How are probability and expected value calculated?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nProbability is calculated by dividing the number of successful outcomes by the total number of possible outcomes. Expected value is calculated by multiplying each outcome by its probability and summing up these values.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_How_are_probability_and_expected_value_used_in_decision_making\"><\/span>3. How are probability and expected value used in decision making?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nProbability and expected value help in evaluating the risks and rewards associated with different outcomes, enabling individuals to make more informed decisions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Can_probability_and_expected_value_be_applied_in_real-life_situations\"><\/span>4. Can probability and expected value be applied in real-life situations?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, probability and expected value are widely used in fields such as finance, insurance, and sports analysis to predict outcomes and make informed decisions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_How_does_Investigation_2_contribute_to_statistical_understanding\"><\/span>5. How does Investigation 2 contribute to statistical understanding?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nInvestigation 2 provides a foundation for understanding essential statistical concepts, allowing students to explore more advanced topics later on.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_How_do_probability_distributions_relate_to_Investigation_2\"><\/span>6. How do probability distributions relate to Investigation 2?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nProbability distributions represent the range of possible outcomes and their associated probabilities, which are explored in Investigation 2 to understand the likelihood of different events.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_Can_expected_value_be_negative\"><\/span>7. Can expected value be negative?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, expected value can be negative if the potential losses outweigh the potential gains in a given scenario.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_are_some_other_applications_of_probability_and_expected_value\"><\/span>8. What are some other applications of probability and expected value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nProbability and expected value are used in risk assessment, stock market analysis, weather prediction, and various other fields where predictions and decision making are essential.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_How_does_Investigation_2_enhance_critical_thinking_skills\"><\/span>9. How does Investigation 2 enhance critical thinking skills?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nInvestigation 2 requires analyzing data, making predictions, and evaluating the likelihood of outcomes, which develops critical thinking abilities.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_What_is_the_significance_of_gamble_situations_in_Investigation_2\"><\/span>10. What is the significance of gamble situations in Investigation 2?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nAnalyzing gamble situations helps students understand the concept of expected value and apply it to decision making involving risks and rewards.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Can_probability_and_expected_value_be_used_to_predict_events_accurately\"><\/span>11. Can probability and expected value be used to predict events accurately?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nWhile probability and expected value provide insights into likely outcomes, they do not guarantee absolute accuracy as future events can be influenced by random factors.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_How_can_probability_and_expected_value_improve_our_daily_lives\"><\/span>12. How can probability and expected value improve our daily lives?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nUnderstanding probability and expected value enables individuals to make more informed decisions, evaluate risks, and predict outcomes in various real-life situations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Probability and expected value are essential concepts in the field of statistics. Investigation 2 focuses on these concepts and aims to provide a deeper understanding of their applications. By exploring various scenarios and conducting experiments, students can gain valuable insights into how probability and expected value play a crucial role in decision making and prediction. &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What do you expect probability and expected value Investigation 2?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-do-you-expect-probability-and-expected-value-investigation-2\/#more-261432\">Read more<span class=\"screen-reader-text\">What do you expect probability and expected value Investigation 2?<\/span><\/a><\/p>\n","protected":false},"author":66,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-261432","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What do you expect probability and expected value Investigation 2?<\/title>\n<meta name=\"description\" content=\"Probability and expected value are essential concepts in the field of statistics. 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