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

Step-by-step 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       78Total

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