2. Complete the PDF.

x	P(X = x)	x P(X = x)
0	0.1
1	0.4
2
3	0.2

Part (a)

Find the probability that X = 2.

Part (b)

Find the expected value.

3. The probability that a certain hockey team will win any given game is 0.3787 based on their 13 year win history of 392 wins out of 1035 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November. What is the probability that the hockey team wins 5 games in November? (Round your answer to four decimal places.)

4. The probability that a certain hockey team will win any given game is 0.3808 based on their 13 year win history of 393 wins out of 1032 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November. Find the probability that the hockey team wins at least 6 games in November. (Round your answer to four decimal places.)

5. The probability that a certain hockey team will win any given game is 0.3836 based on their 13 year win history of 397 wins out of 1035 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November. What is the expected number of wins for the month of November? (Round your answer to two decimal places.) wins

6. The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 8-year period. Assume each year is independent.

Part (a)

In words, define the Random Variable X.

the yearly income of a personthe number of audits a person who has an income over $25,000 receives in a 8-year period the number of audits the IRS does each yearthe number of audits the IRS does every 8 years for a person who has an income over $25,000

Part (b)

List the values that X may take on.

X = 1, 2, 3, ...X = 1, 2, 3, ..., 98, 99, 100 X = 0, 1, 2, ..., 7, 8X = 1, 2, 3, ..., 7, 8

Part (c)

Give the distribution of X. X ~

Part (d)

How many audits are expected in a 8-year period? (Round your answer to two decimal places.) audits

Part (e)

Find the probability that a person is not audited at all. (Round your answer to four decimal places.)

Part (f)

Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)