Problem: The pdf function

Problem

$X$ is a discrete random variable with range $x_1=-1, x_2=1, x_3=4$ . Also, $P\left( X=-1 \right)=1/4$ , $P\left( X=1 \right)=1/2$ and $P\left( X=4 \right)=1/4$ . $f$ is the probability mass function and $F$ is the cumulative distribution function for $X$ .

1. Find $f(1)$
2. Find $f(2)$
3. Find $P(X≤2)$
4. Find $P(-1<X≤4)$
5. Show that $f\left( -1 \right)+f\left( 1 \right)+f\left( 4 \right)=1$ . Explain why this must be the case?
6. Find $F(-1)$
7. Find $F(1)$
8. Find $F(0.999)$