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We know, or else, it is not hard to prove, that if X and Y are independent standard normal random variables, then X + Y and X - Y are independent. This problem is devoted to a converse. Suppose that X and Y are independent symmetric random variables with mean 0 and variance 1, such that X + Y and X - Y are independent. Let ? denote the common characteristic function of X and Y. Prove, along the following path, that X and Y must be standard normal random variables:
(a) Prove that ?(2t)=(?(t))4.
(b) Iterate.
suppose the estimated slope coefficient in a regression model measuring the association between the independent
Prior to conducting this experiment, the manager believed the variance in inspection errors was lower for experienced inspectors than for novice inspectors. Do the sample data support her belief? Test using α = .05.
Assert with probability of at least 0.95 that the error of her estimate will not exceed 0.07. How large a sample, n, will she require if she has no idea what the true proportion is.
Let Nt,t=0 be a Poisson process with intensitya. Let X be a random variable, independent of the Poisson process Nt, meaning that X is independent.
A fashion student was interested in factors that predicted the salaries of catwalk models. She collected data from 231 models.
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at a baby shower we were discusing baby statistcs. one women told us she had read a report that for every 100 babies
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The variance of some data is 37.33 what is the standard deviation?
there is a 57 chance of failing a course w out a tutor and a 27 chance w a tutor. the chance of finding a tutor is
Regress M on GDP and test for autocorrelation at the 5% level of significance and Correct for autocorrelation if it is found in part a.
A regression analysis was carried out of returns on stocks (Y) versus the ratio of book to market value (X).
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