Find the mean and variance of Y.

1.   After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.

 

a.   Let X = 1 if successful, X = 0 if not. Find the mean and variance of X.

b.   If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.

c.    Find the mean and variance of Y.

 

 

2.    A certain brand of dinner ware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise.

 

a.   Let pX denote the success probability for X.

b.  Find pX . Let pY denote the success probability for Y.

c.    Find pY . Let pZ denote the success probability for Z.

d.  Find pZ . Is it possible for both X and Y to equal 1?

e.  Does pZ = pX + pY?

f.      Does Z = X + Y? Explain.

 

 

3.    When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise.

a.   Let pX denote the success probability for X. Find pX .

b.  Let pY denote the success probability for Y. Find pY

c.    Let pZ denote the success probability for Z. Find pZ .

d.  Is it possible for both X and Y to equal 1?

e.  Does pZ = pX + pY?

f.     Does Z = X + Y? Explain.

find the cost of your paper

What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….