IF X is a discrete random variable whose possible values are

IF X is a discrete random variable whose possible values are 1,2,3 and 4 and the mass function p(x) is proportional to 1/x find EX. I know I have to take take each x times its propability but I am unsure how to get each proabbailty for each value. The answer is 1.92

Solution

Here,

P(x) = c/x

Normalizing the sum to 1,

P(1) + P(2) + P(3) + P(4) = 1

c/1 + c/2 + c/3 + c/4 = 1

2.083333333c = 1

c = 0.48

Thus,

P(x) = 0.48/x

Consider the table:

Thus,

E(x) = Expected value = mean =    1.92 [ANSWER]