You randomly call friends who could be potential partners for a dance. You think that they all respond to your requests independently of each other, and you estimate that each one is 7% likely to accept your request. Let X denote the number of phone calls that you make to successfully get a date.
a. Find the expected number of people you need to call, i.e., E(X).
b. Find the variance of the number of people you need to call, i.e., Vai(X).
c. Given that the first 3 people do not accept your invitation, let Y denote the additional number of people you need to call (Y does not include those first 3 people); i.e., suppose X > 3 is given, then let Y = X - 3. Under these conditions, what is the mass of Y?