Consider three random variables X is a mixture of a uniform

Consider three random variables: X is a mixture of a uniform distribution on the interval 0-2 and a uniform distribution on the interval 0-3; Y is the sum of two random variables, one is uniform on 0-2 and the other is uniform on 0-3; Z is a normal distribution that has been right censored at 1. Match these random variables with the following descriptions: Both the distribution and density functions are continuous. The distribution function is continuous but the density function is discontinuous. The distribution function is discontinuous.

Solution

a)

the random variable : X because it is uniform

b)

the random variable : Z because it is normal

c)

the random variable : Y because it is the sum of 2 uniform