Question

Consider a random variable X with the following probability distribution:

x p(x)
-6 1/6
0 2/3
6 1/6

Let Y = X².

E(X) is equal to

Answer 1

The expected value E(X) of the given probability distribution is 0, calculated by summing the products of each value of X and its corresponding probability.

Step-by-step explanation:

The student is asking about the expected value (also known as the mean) of a random variable X with a specific probability distribution. The expected value E(X) is calculated by multiplying each possible value of X by its corresponding probability and summing all those products. However, the question also introduces a transformation of the variable X, called Y, which is defined as Y = X². To find E(X), one would use the formula:

E(X) = (− 6 × 1/6) + (0 × 2/3) + (6 × 1/6)

When calculated, E(X) would be the sum of those products, which in this case simplifies to:

E(X) = (− 6 × 1/6) + (0 × 2/3) + (6 × 1/6) = − 1 + 0 + 1 = 0

Thus, the expected value of X is 0.