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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.
In baseball, a "no-hitter" is a regulation 9-inning game in which the pitcher yields no hits to the opposing batters. Chance (Summer, 1994) reported on a study of no-hitters in Major League Baseball (MLB).
Calculate, test, and interpret the relationship between two variables using the correlation coefficient.
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Data from a National Health Survey show that men's average weight is normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.
At the end of the Halloween Festival the organizers estimated that a family of participants spent in average $50.00 with a standard deviation of $15.00. If 49 participants (49 = size of the sample) are selected randomly, what's the likeihood that ..
Drug manufacturer knows that for a certain antibiotics, the average number of doses ordered for a patient is 20. Steve Simmons, a salesman for the company
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Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.
Determine equation in point-intercept form for line that goes through points (8,-1) and (4,3).
The Graduate Management Admission Council, who administers the test, claims that the mean total score is 529. Suppose a random sample of 8 students took the test, and their scores are given below. 699, 560, 414, 570, 521, 663, 727, 413 Use α = .05..
Describe the situation and the variables and determine whether the variables are normally distributed or not. How could you change these to a normally distributed dataset?
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