Question

Let x be a normal random variable with mean 0 and variance 1, then the expected value of x is?

Answer 1

The expected value or mean of a normal random variable x with mean 0 and variance 1 is -0.2.

Step-by-step explanation:

The expected value or mean of a normal random variable x with a mean of 0 and variance of 1 can be calculated using the formula: E(x) = μ = Σ xP(x), where μ represents the expected value. In this case, the possible values of x are -1, 0, and 1, and the corresponding probabilities are 0.5, 0.2, and 0.3 respectively. So, substituting these values into the formula, we have: E(x) = ( -1 × 0.5) + (0 × 0.2) + (1 × 0.3) = -0.5 + 0 + 0.3 = -0.2.