sillybuffalo
New member
- Joined
- Sep 18, 2013
- Messages
- 9
a) Let X have a Poisson probability distribution with mean λ=6. Once you observe X, toss a fair coin X times and let Y be the number of heads that show. Find the probability that Y=4.
b) Let the Poisson random variable X above have an arbitrary mean λ>0 and find the probability that Y=y for every integer y≥0, where once again Y is the number of heads in X throws of a fair coin.
I'm really lost with this problem, but to start with Part A, I think that I'm supposed to do something along the lines of...
P(Y=4|X) * P (X = some value)
I believe that Y has a binomial probability distribution (since we're flipping coins) and X has a Poisson probability distribution (as stated in the problem). Any further insight?
b) Let the Poisson random variable X above have an arbitrary mean λ>0 and find the probability that Y=y for every integer y≥0, where once again Y is the number of heads in X throws of a fair coin.
I'm really lost with this problem, but to start with Part A, I think that I'm supposed to do something along the lines of...
P(Y=4|X) * P (X = some value)
I believe that Y has a binomial probability distribution (since we're flipping coins) and X has a Poisson probability distribution (as stated in the problem). Any further insight?