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Suppose G is n×n non-negative definite, and α is n×1.
(a) Find an n×1 vector U of normal random variables with mean 0 and cov(U) = G. Hint: let V be an n×1 vector of independent N(0, 1) variables, and let U = G1/2V.
(b) How would you modify the construction to get E(U ) = α?
Find the expected value when you pick 4 and when you pick 5, betting $1 each time. Based on your results from parts a and b, are you better off picking 4 numbers or picking 5? Explain your reasoning.
consider the following joint probability density function of the random variables x and y fxy 3x-y9 for 1ltxlt3 and
suppose xis a random variable with mean -5 and variance 2. what can you say about the probability that x deviates from
let x be a continuous distribution with probability density function fx2 x32 if xgt -2 and fx0 otherwiselet yx2.
Consider these data as random samples from two independent normal populations; carry out an appropriate test to con?rm or refute the hypothesis that instrument 2 is less precise than instrument 1.
among eighteen computers in some store six have defects. five randomly selected computers are bought for the university
Construct a probability for the number of students in the sample who watch soap operas.
In the 18th century, the Chevalier de Mere asked Blaise Pascal to compare the probabilities of two events. Below, you will compute the probability of the two events that, prior to contrary gambling experience, were thought by de Mere to be equally..
the percentage of all people with an sat score above the score you calculated in a is of course 5 but what percentage
Rhode Island Red Chickens the incubation time for Rhode Island Red chicks is normally distributed to find out the number of chicks we expect that will hatch.
suppose that two electronic components in the guidance system for a missile operate independently and that each has a
Determine new, standardized score for each of following values from original population.
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