Prove that the Px(x) is probability mass function
Px (x)=( I\14 x^ 2 if x £[1,2,3,4])
0. Otherwise
To prove that Px(x) is a probability mass function, we need to show two things:
1. Px(x) is non-negative for all x: Since Px(x) = 1/4x^2 for x that belong to the set {1,2,3,4} and Px(x) = 0 for all other values of x, Px(x) is non-negative for all x.
2. The sum of Px(x) over all possible values of x is equal to 1:
Px(1) = 1/4(1)^2 = 1/4
Px(2) = 1/4(2)^2 = 1
Px(3) = 1/4(3)^2 = 9/4
Px(4) = 1/4(4)^2 = 4
Therefore, the sum of Px(x) over all possible values of x is:
Px(1) + Px(2) + Px(3) + Px(4) = 1/4 + 1 + 9/4 + 4
= 1/4 + 1 + 9/4 + 16/4
= (1 + 4 + 9 + 16) / 4
= 30 / 4 = 7.5
Since the sum of Px(x) over all possible values of x is not equal to 1, Px(x) is not a probability mass function.