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:Step-by-step explanation:Given that  uneven die with 8 faces with numbers 1 through 8the probability of each number coming up is proportional to the number itself.P(x)= kx, x =1,2,3...8To find k:Since total probability =1we have \Sigma_1^10 kx =1Simplify to get36k =1:  k = 1/36Hence 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