Question

Define Mathematical expectation in terms of a discrete random variable.

Answer 1

Let X be a discrete random variable with probability mass function (p.m.f) P(x). Then, its expected value is defined by E(X) = ∑_Xxp(x) In other words, if x₁ , x₂ , x₃ ,…… x_n are the different values of X, and p(x₁ ), p(x₂ ) …..p(x_n ) are the corresponding probabilities, then E(X) = x₁ p(x₁ ) + x₂ p(x₂ ) + x₃ p(x₃ ) +… x_n p(x_n ).