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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)?
Using the .05 level, do the results support the researcher's theory? (a) Use the steps of hypothesis testing, (b) sketch the distributions involved.
A cut-off time is set at the slowest 10% of the learning distribution. Anyone slower than this cut-off time is definitely not hired. What proportion of the candidates will be hired automatically?
A case-control study of relationship between liver cirrhosis among both non alcoholics and alcoholics. Describe whether smoking is confounder.
Suppose a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit hour courses
Shouldn"t say never, two have made it from maybe twenty. This one makes it, Does anyone know what the popular vote was.? What was the percentage for each leader?
an index of two store items for 2007 based on 2004 is to be constructed. the information for the prices and quantities
Which measure of association would the researcher use to compare the relationship between the IV and DV? Why?
a pollster collects the following data for 350 college
Consider the following portion of an electric circuit with three relays. Current will flow from point A to point B if there is at least one closed path when the relays are activated. The relays may malfunction and not close when activated.
consider a simple card game where there are four cards labeled 1 2 3 and 4. each round my friend first draws a card
A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of the components ..
A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 12 hours, with a standard deviation of 3.0 hours.
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