Question

Customers depart from a bookstore according to a Poisson process with a rate λ per hour. Each customer buys a book with probability p, independent of everything else.

a. Find the distribution of the time until the first sale of a book

b. Find the probability that no books are sold during a particular hour

c. Find the expected number of customers who buy a book during a particular hour

Answer 1

Answer:

a)

Given,

likelihood = p

rate = every hour

To give the circulation of time until the primary offer of a book

Consider,

holding up time can be given as follows

i.e.,

f(x) = pe^-px

b)

Presently to give likelihood that no books are sold during a specific hour

i.e.,

P(y = 0) = e^-p

c)

To give the normal number of clients who purchase a book during a specific hour

Consider,

Poisson distribution E(y) = p