<\/span><\/h2>\nTo find the expected value of x statistics, follow these steps:<\/p>\n
**Step 1: Identify the random variable:** Determine the variable you are interested in, which is often denoted as X.<\/p>\n
**Step 2: Assign probabilities:** Determine the probabilities associated with each value of the random variable X. This step is essential for discrete random variables, as they have a finite number of possible outcomes.<\/p>\n
**Step 3: Multiply each outcome by its respective probability:** Multiply each value of X by its corresponding probability. This step is necessary to give more weightage to values that occur more frequently.<\/p>\n
**Step 4: Sum all the products:** Add up all the products obtained in the previous step. The result will be the expected value of X.<\/p>\n
**Example:** Let’s consider a simple example to illustrate the process. Suppose we have the following probabilities and values of a random variable X:<\/p>\n
“`
\nValue of X: 1 2 3 4
\nProbability: 0.2 0.3 0.1 0.4
\n“`<\/p>\n
To find the expected value:<\/p>\n
Step 1: Identify X as the random variable.<\/p>\n
Step 2: Assign probabilities: The probability of X=1 is 0.2, X=2 is 0.3, X=3 is 0.1, and X=4 is 0.4.<\/p>\n
Step 3: Multiply and sum: Multiply each value of X by its corresponding probability and sum the products: (1 * 0.2) + (2 * 0.3) + (3 * 0.1) + (4 * 0.4) = 0.2 + 0.6 + 0.3 + 1.6 = 2.7.<\/p>\n
Therefore, the expected value of X, E(X), is 2.7.<\/p>\n
<\/p>\n