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A better model for the sailboat race of Problem 5.5.4 accounts for the fact that all boats are subject to the same randomness of wind and tide. Suppose in the race of ten sailboats, the finishing times Xi are identical Gaussian random variables with expected value 35 minutes and standard deviation 5 minutes. However, for every pair of boats i and j, the finish times Xi and Xj have correlation coefficient ρ = 0.8.
(a) What is the covariance matrix of X = [X1 ··· X10]?
(b) Let
Denote the average finish time. What are the expected value and variance of Y? What is P[Y ≤ 25]?
Problem 5.5.4
In a race of 10 sailboats, the finishing times of all boats are iid Gaussian random variables with expected value 35 minutes and standard deviation 5 minutes.
(a) What is the probability that the winning boat will finish the race in less than 25 minutes?
(b) What is the probability that the last boat will cross the finish line in more than 50 minutes? (c) Given this model, what is the probability that a boat will finish before it starts (negative finishing time)?
For planning purposes, the hospital physician staff wold like to know the probability that a given patient is a smother is the patient has a serious illness.
Is there enough evidence to support the consumers conjecture at a=0.05. First, indentify the alternative and the null hypotheses.
a. Determine the sample proportion, p, of households with cellular telephones that can be used to access the Internet. b. If the population proportion is 0.40, determine the standard error of the proportion.
Use the interaction plot to argue that the new design is less sensitive to changes in environmental conditions (temperature and humidity). What limitations apply to this argument?
Assuming the sample size of 40 can be considered as large, compute the confidence interval for a confidence level of 90%.
suppose we know grades on final exam in a statistic course are normally distributed with a mean of 72 and standard
Let X 1 , X 2 , X 3 , X 4 be a random sample from a Poisson distribution with parameter λ and let Y = X 1 + X 2 + X 3 + X 4 . You decide to test λ = 1.60 versus λ
The length of a particular telemarketing phone call has an exponential distribution with a mean equal to 1.5 minutes. Find the probability that the length of a randomly selected call will be between 30 - 50 minutes and 1 minuter or longer.
test for single proportion.one kind of plant has only blue flowers and white flowers. according to a genetic model the
in boston record game fishes it is stated that in the cozumel region approximately 40 of strikes while trolling result
Hemantis-Beckersky Case Study Retention of Finance Workforce
Determine the expected value and standard error of the sum of 400 draws?
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