You are a sales rep, and receive phone messages that 2 of your 4 major customers need to talk to you about making a major purchase. unfortunately, neither one identified themselves or left a callback number. so you will call them back in no particular order until you find one of the interested customers. let x= {1, 2, 3, 4} stand for which of your calls finally talks to one of the interested customers. a) write down a table of the probability mass function p(x) = p(x = x) for which call reaches the first interested customer. b) calculate the expected number of calls e(x) you will have made when you talk to the first interested customer.

a) the probability mass function p(x) = P(X=x) is:

b)  The expected number of calls E(X) you will have made when you talk to the first interested customer is 1.667 calls

Step-by-step explanation:

The probability that you will talk with one of the interest customers at the first call is:

Because, you have 4 possibles customers and 2 of them are interested.

Also, the probability that you will talk with one of the interest customers at the second call is:

Because, in the first call you are going to talk with one customer that it is not interested, so you have 4 possibles customers and 2 of then are not interested. Then, for the second call, you are going to talk with one customer that it is interested, so, now, you have 3 possibles customers and 2 of them are interested.

At the same way, the probability that you will talk with one of the interest customers at the third call is:

Finally, taking into account that there are 4 customers and 2 of them are interested, the maximum number of calls for find the first customer interested is 3, so P(4) is zero.

So, the probability mass function p(x) = P(X=x) is:

Then, the expected value is calculated as:

Where are the possible values of the variable and are their respectives probabilities.

Therefore, the expected number of calls that you will have made when you talk to the first interested customer is:

E(x)=1(0.5) + 2(0.333) + 3(0.166) + 4(0) = 1.667

2425

step-by-step explanation: