Question

Joey Louzeshot is practicing his dart throwing skills. In the past, he hits the bullseye on the target only one time for every 200 throws. To practice, he will throw darts on Sunday and Monday.

e) On Monday, Joey will practice by throwing the dart until hits the bullseye, then he will quit practicing. Let A be the number of attempts until he hits the bullseye. What are the distribution, parameter(s) and support of A?

f) What is the expected value and standard deviation of A?

Answer 1

Geometric Distribution:

Assume Bernoulli trials — that is, (1) there are two possible outcomes, (2) the trials are independent, and (3) p, the probability of success, remains the same from trial to trial. Let X denote the number of trials until the first success. Then, the probability mass function of X is:

for x=1,2,3,...........

In this case 'X' follows Geometric Distribution.

Expected Value of X :

Standard Deviation of X=  

Given,

Joey Louzeshot , hits the bullseye on the target only one time for every 200 throws

Probability of Joey Louzeshot hits the bulleye = 1/200 = 0.005

A : Number of attempts until he hits the bulls eye.

Hitting bulls eye is success.

e) A : Number of ateempts until he hits the bulls eye(Success) follows geometric distribution with Probability mass function:

for a 1,2,3,4,.....................................

f)

Expected value of A = 200

Standard Deviation of A=  

Standard Deviation of A= 199.4994