Bernoulli Distribution Question

[abc4616]

Suppose a coin is tossed until a head appears. Let p be the probability of a head on any given toss. Define random variable X to be the number of tosses required to obtain a head.

a) State the set of values that X can take on. Is this finite or countably infinite set?
b) What is the PMF (probability mass function) of X? If p = 1/4, what is the probability that X=10?

Can any one help on this question??

 

[pka]

If P(H=n) is the probability that the first head shows on the nth flip is \(\displaystyle P(H = n) = \left( {\frac{1}{2}} \right)^n.\) This is certainly countably infinite.

Assuming that b) is a continuation of a) with change p=1/4, then the answer is \(\displaystyle P(H = n) = \left( {\frac{3}{4}} \right)^{n - 1} \left( {\frac{1}{4}} \right)\)