Question

we have an uneven die with 8 faces with numbers 1 through 8. the probability of each number coming up is proportional to the number itself. for example the probability of 2 coming up is twice the probability of 1 coming up, and so on. find PMF of x

Answer 1

Explanation:

Given that uneven die with 8 faces with numbers 1 through 8

the probability of each number coming up is proportional to the number itself.

P(x)= kx, x =1,2,3...8

To find k:

Since total probability =1

we have \Sigma_1^10 kx =1

Simplify to get

36k =1: k = 1/36

Hence distribution of X is as follows:

x 1 2 3 4 5 6 7 8 Total

p(x) 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2/9 1