Question

Q3. Suppose we toss a coin until we see a heads, and let X be the number of tosses. Recall that this is what we called the geometric distribution. Assume that it is a fair coin (equal probability of heads and tails).

1. What is the p.m.f. of X? (I.e., for an integer i, what is P(X=i)?

2. What is ?[X]? ({} this is a discrete variable that takes infinitely many values.)

Answer 1

1. What is the p.m.f. of X? (I.e., for an integer i, what is P(X=i)

Ans :It is a geometric distribution with p=0.5.

P(X=i) = p(1-p)^i-1 = 0.5*0.5^i-1 = 0.5ⁱ ( i=1,2,3,...)

1. What is ?[X]? ({} this is a discrete variable that takes infinitely many values.