An octahedral die has eight faces numbered from 1 to 8. The random variable X is the score obtained when the die is thrown. The bias of the die is such that P(X = r) = c for r = 1, 2, 3, 4, 5 P(X = r)...

An octahedral die has eight faces numbered from 1 to 8. The random variable X is the score
obtained when the die is thrown. The bias of the die is such that
P(X = r) = c for r = 1, 2, 3, 4, 5
P(X = r) = d for r = 6, 7, 8
P(X < 6)="P(X" ≥="">
(i) Compute the values of c and d.
(ii) Estimate that E(X) = 5 and find the variance of X.
(iii) The die is thrown twice. Calculate the probability that the sum of the two scores is 10.
(iv) The random variable Y is the sum of the scores when the die is thrown 48 times.
Measure the mean and variance of Y.
(v) Assuming that Y has a normal distribution, write the probability that Y lies between 220
and 260 inclusive.