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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.
Given length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation five feet, what is the probability he throws it: Between 50 feet and 60 feet.
Assume the population proportion is 0.17 and a simple random sample of 850 households will be selected from the population. What is the probability that the sample proportion will be within ±0.02 of the population proportion?
What information is provided by the numerical value of the Pearson correlation? For the following scores, compute the Pearson correlation:
A teacher wants to know if students in her biology class did significantly better on an exam after instruction using authentic learning. The scores pre and post test are listed below. Based on an α = .05, what can the teacher conclude?
You are given an annual time series with 40 consecutive values and asked to fit a fifth-order autoregressive model.
Normalized matrix for one decision criterion at Firm T is given below.
The estimated miles per gallon ratings of a class of automobiles are normally distributed with a mean of 12.8 and a standard deviation of 3.2. What is the probability that one of these automobiles selected at random would get:
The heights of young women are approximately normal with mean 65 inches and standard deviation 2.5 inches.
You are investigating the flight characteristics of different kinds of birds. You collect a sample of 33 European swallows (Hirundo rustica) and measure their air-speed velocity in a borrowed wind tunnel.
As sample size increases, the standard error of M _______________ .
Find a 95% confidence interval for the proportion p of the inner-city, working-class group who eventually became alcoholics.
Determine which crew should be sent to each city to minimize the total distance traveled. How many miles will be traveled if these assignments are made?
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