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1. A player throws a fair coin and wins $1 each time it's heads, but loses $1 each time it's tails. The player will stop when his or her net winnings reach $1, or after n throws, whichever comes sooner. What is the player's probability of winning, and expected loss conditional on not winning, if (a) n = 3? (b) n = 5?
2. Let α be a stopping time and τ (n) a nondecreasing sequence of bounded stopping times, both for a martingale {Xn, Bn }n≥1. Show that α is also a stopping time for the martingale {Xτ (n), Bτ (n)}n≥1, in the sense that {α ≤ τ (n)}∈ Bτ (n) for each n.
Discuss the fields in which Poisson distribution is applied. Why does it matter whether a population of arrivals is limited or unlimited?
Find the 95% confidence interval of the mean number of ER patients treated each day at the hospital.
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If the residual plot, i.e., a graph in which the residuals for a particular regression model are plotted along with their associate value of x as an ordered pair, shows a parabolic pattern, which of the following assumptions of the simple regressi..
Determine and interpret the p-value for the test. Construct and interpret the 99% confidence interval for the test. Source: U.S. Bureau of Labor Statistics, Consumer Expenditure Survey, Interview Survey, annual.
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations. What is the probability that all six arrive within 2 days
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A professor asked her sophomore students, "How many drinks do you typically have per session? (A drink is defined as one 12oz beer, one 4oz glass of wine, or one 1oz shot of liquor.)"
To recognize the width of the confidence interval.As the confidence level \"1 - α\" increases, the width of the confidence interval.
suppose that you wanted to determine if the males in your sales force differed from the females in your sales force in
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