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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.
a researcher selects a sample of 6 professors 6 students and 6 administrators at a local school and has them rate the
a scientist is proposing a study on the level of violence in teenagers. he feels that the boys are more violent than
Using a random sample of 100 newly-packed Chococake, it is found that the mean shelf life is 154 hours. Can the cake house manager conclude that the new packaging technique is efficient at 0.01 significance level?
A newspaper ad for a manager trainee position contained the statement "Our manager trainees have a first-year earnings average of $20,000 to $24,000." Do you think that the ad is describing a confidence interval? Explain your answer.
Identify the Odds Ratio and the significance of the Odds Ratio for each of the covariates. How has the relationship between Chole_Cat and Hypertension changed with the addition of the other variables?
Derive the steady-state condition in terms of the equilibrium capital stock per person, k∗, starting from the law of motion for total capital, in a Solow model with positive population growth.
As part of an opinion survey, a simple random sample of 1,500 families is chosen. What is the chance that between 9% and 11% of the sample families will not own cars?
The port of Trop can service only 1 ship at a time. However, there is mooring space for 3 more ships. Trop is a favorite port of call, but, if no mooring space is available the ships have to go to the next port.
Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?
a statewide real estate agency old colony specializes in residential home sales in nothern pa. records indicate the
Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.
A researcher finds a correlation between self esteem and shyness is -0.50, which is significant for his sample. Interpret this correlation.
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