Question

If the range of the random variable $X$ is from $-\alpha$ to $+\alpha$ , the limits of $F\left(X\right)$ are

• A. $0$ to $\alpha$
• B. $-\alpha$ to $3$
• C. $-1$ to $+1$
• D. $0$ to $1$

Answer 1

Answer: (D)

$0$ to $1$

We have for a random variable $X$,
$F\left(x\right)=P(X\le x)=0$ for $x<0$ (since the random variable cannot assume negative values, so its probability is 0)
$F\left(x\right)=P(X\le x)$ for $x\ge 0$
Since, the value of probability lies between 0 and 1.
So, $0<F\left(x\right)\le 1$
Hence, limits of $F\left(x\right)$ are 0 to 1.