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

The cumulative distribution function (CDF) of a random variable $X$ is defined as:

Given:

• $P(X = -1) = 0.5$

• $P(X = +1) = 0.5$

Calculating the CDF at the given points:

1. At $x = -1$:

2. At $x = +1$:

Thus, the values of $F(x)$ at $x = -1$ and $x = +1$ are 0.5 and 1 respectively (Option C).