Question

A company offers prizes to their employees depending on the time it takes them to complete an assignment. Employees receive a 300, 200 or 100 euros gratification if the assignment is completed in less than 10 hours, between 10 and 15 hours or in more than 15 hours, respectively. The probability of completing the task in each of these cases is 0.1, 0.4 and 0.5 respectively.

a) Find the probability distribution function, the cumulative probability function and the expected value of the random variable X = “prize received by the employee”.

b) Consider a random variable Y , that takes value 1 when a randomly selected employee completes the assignment in less then 10 hours and value 0 in all other cases. Find the probability distribution function, the cumulative probability function and the expected value of the random variable Y .

c) A group of 10 employees is selected, what’s the probability that at least 2 complete the assignment in less than 10 hours?

d) The company has a total of 190 employees and can, at most, reward 10 employees that complete the task in less than 10 hours, find the probability that the company cannot pay all rewards.

Answer 1