Question

Bob has two coins, A and B, in front of him. The probability of Heads at each toss is p=0.5 for coin A and q=0.9 for coin B.Bob chooses one of the two coins at random (both choices are equally likely).He then continues with 5 tosses of the chosen coin; these tosses are conditionally independent given the choice of the coin.
Let:
Hi :the event that Bob's ith coin toss resulted in Heads;
N :the number of Heads in Bob's coin tosses.
1.For i={0,1,..,5},PN(i), the PMF of N, is in the form 1/2(5Ca)b^5 +C(5Cd)q^e(1-q)^f. Find the coefficients a,b,c,d,e,f. Your answer can be either a number or an expression involving i
2. E[N]
3.Find the conditional variance of N, in a conditional model where we condition on having chosen coin A and the first two tosses resulting in Heads. Var(N| A,H1,H2)
4.Are the events H1 and {N=5} independent?
Given that the 3rd toss resulted in Heads, what is the probability that coin A was chosen?

Answer 1

can anyone please help me out here?