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).
What is the p.m.f. of X? (I.e., for an integer i, what is P(X=i)?
What is ?[X]? ({} this is a discrete variable that takes infinitely many values.)
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*0.5i-1 = 0.5i ( i=1,2,3,...)
What is ?[X]? ({} this is a discrete variable that takes infinitely many values.
Q3. Suppose we toss a coin until we see a heads, and let X be the...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
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