Question

Suppose you select two numbers at random with replacement from the set {1, 2, 3} and then you form a rectangle with the first number as the length of the rectangle and the second number as the height of the rectangle. Let X be the area of the rectangle so formed. Find the probability mass function of X.

Answer 1

Let X be the rectangular distribution

where X is uniformly distribute(3,1)

b=1

a=1

The PMF will be

f(x)=1/b-a

f(x)=1/3-1

f(x)=1/2

f(x)=0.5