Suppose that a random variable X counts the number of consum

Suppose that a random variable X counts the number of consumers visiting a large department store for a day.

(a) What would be the support of this random variable?

(b) Is X discrete or continuous? Explain why.

(c) Suppose that the probability that no customer visits the store is 0.001, i.e., P(X = 0) = 0.001. Similarly, suppose that P(X = 1) = 0.01, P(X = 2) = 0.01, and P(X = 3) = 0.01. Then, what is the probability that at least four customer visits the store, i.e., P(X 4)?

Solution

a) time can be a support for the variable x

b)discrete, as as some time interval the number of customers can be fluctuating.

c) to find P(X 4) = 1 - P(X<=4)

P(X<=4) = P(X=0) + P(X=1) +P(X=2)+P(X=3)

FROM THE QUESTION PUT VALUES.

= 1- (0.001+0.01+0.01+0.01)

= 0.969