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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 $x=+1$ are

1. 0 and 0.5
2. 0 and 1
3. 0.5 and 1
4. 0.25 and 0.75

Correct answer: 0.5 and 1

Solution

The CDF is $F(x)=P(X\le x)$. Since $P(X=-1)=0.5$, we get $F(-1)=0.5$; and since both $-1$ and $+1$ are included at $x=+1$, $F(+1)=1$.

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