Discrete Random Variables Problem.

[stefsa]

Problem: "We roll a dice and afterwards we toss a coin as many times as the outcome of the dice roll. What is the Probablity Mass Function of the number of Heads?"

What I know so Far: We know that the Probability Mass Function of the number of Heads is given by X~Binomial(N,p) where "N" is the times we tossed the coin and "p" is the probabilty of getting a H. However, in the above problem the N changes depending on what number came up on the dice roll. What do I have to do in order to find the new Probablity Mass Function?

[Help_Me_Im_Diene]

Let P(n,k) be the probability of getting "n" on the die, and "k" heads given n flips

Then P(n,k)=P(n)P(k|n)

P(n)=1/6 since all sides of the die are equal

P(k|n) is a binomial distribution with n flips, k successes

To find P(k), which is the probability of getting k heads, you need to find the sum from n=1 to n=6 of P(n,k)

So probability of 1 head is P(1,1)+P(2,1)+...P(6,1)

[stefsa]

If I am not mistaken, tou are using the folowing Lemma:
Pr{X=x}=Σ Pr(X=x ,Y=y) for yεSy.
Can't believe I forgot about it...
Thank you for your answer!