Question

Let x be a non-negative integer valued random variable. Show that E(x) =

Answer 1

The expected value, or mean, of a random variable can be found by multiplying each value of the random variable by its probability and adding the products.

Step-by-step explanation:

The expected value, or mean, of a random variable X can be found using the formula E(X) = Σ xP(x), where x represents the values of the random variable and P(x) represents the corresponding probabilities. To find the expected value, multiply each value of the random variable by its probability and add the products.

For example, let's say we have a random variable X with values 0, 1, and 2, and corresponding probabilities of 0.2, 0.3, and 0.5. To find the expected value, we calculate: (0 * 0.2) + (1 * 0.3) + (2 * 0.5) = 0 + 0.3 + 1 = 1.3. Therefore, the expected value of X is 1.3.