Question

5) A sales agent earns a monthly salary that is comprised from a fixed amount of $1,000 and a bonus of $100 for each signed deal. The sales agent believes that the probability to sign a single deal is 0.1, and he has the opportunity to try and sign 100 deals in the next month. Denote by W the next month's salary.

(a) Calculate the expected value of W.

(b) Calculate the standard deviation of W.

Answer 1

(a) $2000

(b) $94.9

Explanation:

The expected $ value of signing 100 deals with probability of 0.1 each is

E(X) = 100*0.1 + 100*0.1 + 100*0.1 + ... + 100*0.1 = 100(100*0.1) = $1000

Along with the fixed amount of $1000, the total next month salary is $2000

As for the standard deviation we can apply the following formula

`\sigma = E(X^2) - E(X)^2`

`\sigma = √(0.1*(100 - \mu)^2 + 0.1*(100 - \mu)^2 + ... + 0.1*(100 -\mu)^2)`

`\sigma = √(0.1*100*(100 - 1000)^2)`

`\sigma = √(10*900^2) = √(9000) = 94.9`