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Question: Calvin and Hobbes play a match consisting of a series of games, where Calvin has probability p of winning each game (independently). They play with a "win by two"" rule: the first player to win two games more than his opponent wins the match. Find the probability that Calvin wins the match (in terms of p), in two di↵erent ways:
(a) by conditioning, using the law of total probability.
(b) by interpreting the problem as a gambler's ruin problem.
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 car dealership is worried that Hondas are getting lower sales than Hyundai. Two independent random samples have been selected 630 observations from population 1 (Hondas) and 610 from population 2 (Hyundai).
during each summer many families spent part of their vacation time at a beach along the east or west coast. due to the
question a researcher is interested in differences in the use of sick days by younger and older adults working for a
a sample of 9 days over the past six months showed that a dentist treated the following numbers of
(a) Show that E [X(X - 1)] = µ(µ - 1) + σ 2 (b) Show that E [(X - c) 2 ] = (µ - c) 2 + σ 2 where c is an arbitrary constant.
suppose that a1 a2 are events such that pa1bgt0. show that a1 and a2 are conditionally independent given b i.e.
Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from sleep disorder? Round your answer to 2 decimal places.
the average serum cholesterol level in a certain group of patients is 240 milligrams. a new medication is designed to
in a class 20 of the students are male and 80 female. among male students 40 wears eye glasses among female students 30
Find an estimate of the model standard deviation, σ.- Predict the apparent porosity percentage for a brick with a mean pore diameter of 10 micrometers.
The sample mean was $22,098 and the standard deviation was $6050. Is there evidence at the 1% significance level that the cost of attendance has increased?
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