Find the conditional and joint pmf

Assignment Help Basic Statistics

Reference no: EM13116675

Joe Lucky plays the lottery on any given week with probability p, independently of whether he played on any other week. Each time he plays, he has a probability q of winning, again independently of everything else. During a fixed time period of n weeks, let X be the number of weeks that he played the lottery and Y be the number of weeks that he won.

(a) What is the probability that he played the lottery on any particular week, given that he did not win on that week?
(b) Find the conditional PMF pY | X (y | x).
(c) Find the joint PMF pX,Y (x, y).
(d) Find the marginal PMF pY (y). Hint: One possibility is to start with the answer to part (c), but the algebra can be messy. But if you think intuitively about the procedure that generates Y , you may be able to guess the answer.
(e) Find the conditional PMF pX | Y (x | y). Do this algebraically using the preceding answers.
(f) Rederive the answer to part (e) by thinking as follows: for each one of the n-Y weeks that he did not win, the answer to part (a) should tell you something.

Reference no: EM13116675

Questions Cloud

What is the effect of a mutation : A signalling pathway in the cell is turned on by phosphorylation, leading to decreases in cell division. What is the effect of a mutation that results in the overexpression of an oncogene coding for a phosphatase that works on this pathway?

How is the behaviour of transformed cells : Normal cells greatly slow their rates of cell division after filling a culture dish with a layer that is one cell deep (a monolayer).

How many grams of acid are present : A chemist dissolves 0.9 g of an unknown monoprotic (one acidic H) acid in water. She finds that 14.6 mL of 0.426 M NaOH are required to neutralize the acid.

Significant differences between fasb and iasb : Describe the most significant differences between the FASB and the IASB. Compare and contrast the conceptual frameworks of the IASB and FASB. Discuss which conceptual framework is more coherent or relevant or applicable and explain why.

Find the conditional and joint pmf : Find the marginal PMF pY (y). Hint: One possibility is to start with the answer to part (c), but the algebra can be messy. But if you think intuitively about the procedure that generates Y , you may be able to guess the answer.

Explain negative effects on the physical environment : The movement to develop and market products designed to minimize negative effects on the physical environment or to improve the environment is known as

How much should be amortized by smith co. for year ended : Smith has decided to write off the franchise over the longest possible period. How much should be amortized by Smith Co. for the year ended December 31, 2008?

Most important concepts about international finance : What are the most important concepts about International Finance? Why? How might you use these concepts in your future work endeavors?

How many seconds would it take to swim : The men's world record for swimming 1500.0 m in a long course pool (as of 2007) is 14 min 34.56 s. At this rate, how many seconds would it take to swim 0.800 miles.

User Account

All Pages