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A certain police officer stops cars for speeding. The number of red sports cars she stops in one hour is a Poisson process with rate 4, while the number of other cars she stops is a Poisson process with rate 1. Assume that these two processes are independent of each other. Find the probability that this police officer stops at least 2 ordinary cars before she stops 3 red sports cars.
A set of 50 data values has a mean of 15 and a variance of 25. Find the standard score of a data value = 30.
We would like to test if the proportion of respondents that support the health care bill is less than 50% (a) what kind of hypothesis test is appropriate?
What is the probability that a soldier is a female?
If a researcher decides to use multiple comparisons in a study with three conditions, what is the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to determine the suggested alpha level.
The Price-to-Earnings ratio (P/E) of a publicly listed profit-making company is defined as the ratio of the stock price of the company to the earnings per share.
If the agency is risk neutral, use a decision tree to determine its best course of action.
Let X and Y have a bivariate normal distribution with parameters u1 = 20, u2 = 40, sigma1^2 = 9, sigma2^2 = 4, and p = 0.6. Find the shortest interval for which 0.90 is the conditional probability that Y is in the interval, given that X = 22.
Formulate a suitable null and alternative hypothesis to test the students' claim that they followed their instructor's recommendation at a 5% level of significance and interpret your findings.
You have two unbiased estimates, e 1 and e 2 , of a quantity with variances V 1 and V 2 respectively, and covariance Cov {e1,e 2 } = C. Form a new unbiased estimate:
Rank the funds by using this alternative measure of risk. Which, if any outperformed the market on the risk-adjusted basis.
Q2 is dummy variable equal to 1 in second quarter and 0 otherwise; and Q3 is final dummy variable equal to 1 in third quarter and 0 otherwise. Determine the Base Quarter?
Suppose that X1,..,Xn form a random sample from the normal distribution with unknown mean M and unknown standard deviation S, and let m and s denote the MLEs of M and S. for the sample size n=17, find a value of k such that P(m > M +ks) = 0.95
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