Question

Suppose a random variable X has a cumulative distribution function given by
F(a) = {0 for a<0, 1/2 for 0<=a<1, 3/5 for 1<=a<2, 4/5 for 2<=a<3,
9/10 for 3<=a<3.5, 1 for 3.5<=a.

a. Find the probability mass function for X.

b. Find the probability that a given observation of the value of X is greater than or equal to 1.5.

Answer 1

I'm confused. I think to answer this question, we need to know the range of your variable a. Does a go from -infinity to +3.5?

Answer 2

Nevermind, I get it.

P(x) = 5/10 for 0<= x < 1
= 1/10 for 1<= x < 2
= 2/10 for 2<= x < 3
= 1/10 for 3<= x < 3.5
= 1/10 for 3.5<= x

P(x>1.5) = 5/10