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 \(F(0.999)\)