Question

3. Fionn observed that 91% of the background checks he processes are for potential employees who have already interviewed. Let X be the number of background checks Fionn processes to get his first background check for a potential employee who has not yet interviewed for the job. Assume that the interview statuses are independent.

(a) Find the probability that the 2nd background check that Fionn processes is the first for which the potential employee has not yet interviewed.

(b) What is the underlying process for the random variable X?

A. Bernoulli Process B. Stochastic Process C. Binomial Process D. Random Process

(c) Suppose Y is the number of potential employees who have already interviewed in a group of 15 employees. How are X and Y different?

Answer 1

P(interviewed) = 0.91

P(not interviewed) = 0.09

a) probability that the 2nd background check that Fionn processes is the first for which the potential employee has not yet interviewed.

then first person is already interviewed and second person is not interviewed = 0.91*0.09 = 0.082 (Acc to Product rule)

b) Underlying process for the random variable X is Binomial Process.

Explanation : A Bernoulli random variable X is a random variable that satisfies P(X=1)=p, P(X=0)=1−p. A canonical example is a coin flip which has p=1/2. In fact, you can think of a Bernoulli random variable is just a weighted coin, which comes up 1 with some probability and 0 otherwise. A binomial random variable with parameters n,pis what you get when you count the number of 1's (successes) that come up in a string of n independent Bernoulli random variables, each with parameter p. Another way to say this is that a binomial random variable is the sum of independent and identically distributed Bernoulli random variables.

c) Y is simple already given as the number of potential employees who have already interviewed in a group of 15 employees.

that is definite value

But X is no of background checks to be done for the people who are already interviewed before the background check is done for the non interviewed potential employee.

means first he did back ground check found he is interviewed,again the same thing happen,next he did check but he is not interviewed -- in this case x=2