Let X be a random variable with cumulative distribution func

Let X be a random variable with cumulative distribution function F(a) = Is X a discrete or continuous random variable? Justify your answer.

Solution

From CDF we have probabilites

P(X=1)=F(1)=0.4

P(X=2)=F(2)-F(1)=0.7-0.4=0.3

P(X=3)=F(3)-F(2)=0.9-0.7=0.2

P(X=4)=F(4)-F(3)=1-0.9=0.1

Here X is discrete random variable.