Discrete Distribution In the die-coin experiment, a fair, standard die is rolled and then a fair coin is tossed the number of times showing on the die. Let N denote the die score and Y the number of heads.
a)I want to find the probability density function of N and b)i want to Find the probability density function of Y.
Answer: How to solve this question? I am working on it.
 A: Answer
a) $g(n)=\frac16 for n \in {[1,2,3,4,5,6]}$ .This is a uniform distribution on {1,2,3,4,5,6}
b) $h(0)=\frac{63}{384},h(1)=\frac{120}{384},h(2)=\frac{99}{384},h(3)=\frac{64}{384},h(4)=\frac{29}{384},h(5)=\frac{8}{384},h(6)=\frac{1}{384}$
I think no explanation is needed to the answer a)
Now, let us proceed to the answer b). To arrive at the final answer, we use binomial probability distribution. The expected value of number of points on the roll of a die is 3.5. The random variable Y(number of heads) takes the value{0,1,2,3,4,5,6}. The probability of 0 number of head in a single toss is 0.5. Likewise the probability of 5 heads in 6 tosses is $\binom{6}{5}(0.5)^6$
So, the probability of 0 heads in single toss, 2 tosses, 3 tosses, 4 tosses, 5 tosses and lastly 6 tosses is 0.5,0.25,0.125,0.0625,0.03125,0.015625 respectively. So its total is 0.984375. 
We should multiply 0.984375 with expected value 3.5. The result devided by 21 (the total of number of points on the roll of a die) we get $\frac{63}{384}$
If we follow this procedure to calculate 1,2,3,4,5,6 number of heads with 1,2,3,4,5,6 number of tosses,we get the probability distribution of number of heads on the number of times showing on the die,a fair standard coin is tossed.
