Methods of Mathematical Statistics

Question

A bag contains 5 coins, one of which has a head on both sides while the other 4 coins are normal. A coin is chosen at random from the bag and tossed 2 times. The number of heads obtained is a random variable, say X. (a) What are the possible values of X? Also tabulate the pmf of X. (Hint: The coin chosen is either normal or with head on both sides. Find the conditional probability of X in each of these two cases. Then use the law of total probability and multiplication rule to find the pmf of X.)

(b) Calculate E(X) and Var(X).

Answer 1

5 coins, 4 normal 1 with 2 heads

pick a coin randomly, toss it twice

what is the expected outcome?

E(x) = 4(1H) +1(2H))/(4+1) = 6/5 heads = 1.2 heads= the expected outcome = the mean= long run average outcome

use the binomial distribution

mean = np

var = npq

sd = sqr(npq)