Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distrib...

Question

Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F_X(x) at x = -1 and x = 1 are

A. 0 and 0.5
B. 0 and 1
C. 0.5 and 1
D. 0.25 and 0.75

Accepted Answer

F_X(-1) = 0.5 and F_X(1) = 1. Answer C. The CDF F_X(x) = P(X <= x) accumulates probability from the left. At x = -1, we include the mass at -1 itself (prob 0.5). At x = 1, we include all mass (prob 0.5 + 0.5 = 1). The CDF of a discrete RV is a right-continuous step function that jumps by P(X=x_k) at each support point x_k.

Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F_X(x) at x = -1 and x = 1 are A. 0 and 0.5 B. 0 and 1 C. 0.5 and 1 D. 0.25 and 0.75