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Let U, V, and W be independent standard normal random variables (that is, independent normal random variables, each with mean 0 and variance 1), and let X=3U+4V and Y=U+W. Give a numerical answer for each part below. You may want
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Let U, V, and W be independent standard normal random variables (that is, independent normal random variables, each with mean 0 and variance 1), and let X=3U+4V and Y=U+W. Give a numerical answer for each part below. You may want
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Statistics
In a population, heights of males are normally distributed with u=180 cm and sigma^2=16 cm^2, while the heights of females are normally distributed with u=170 cm and sigma^2= 25 cm^2. a) One random male and one random female are
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Suppose we take a random sample of size n from a normal population with variance, σ2 . It can be shown that (n−1)s2/σ2 has a chisquare distribution with n−1 degrees of freedom, where s is the sample variance. Below is a
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In this problem, you may find it useful to recall the following fact about Poisson random variables. Let X and Y be two independent Poisson random variables, with means λ1 and λ2, respectively. Then, X+Y is a Poisson random
asked by Anonymous on December 16, 2018 
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Let X1,X2,…,X25 be random sample ~ normal(0,16) and Y1, Y2,…,Y25 be random sample ~ normal(1,9), assume the two samples are independent ,comput P(X>Y) where X=Sum(Xi)/25 and Y=Sum(Yi)/25
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Let X and Y be two independent Poisson random variables, with means λ1 and λ2, respectively. Then, X+Y is a Poisson random variable with mean λ1+λ2. Arguing in a similar way, a Poisson random variable X with parameter t, where
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A simple random sample of cars in a city was categorized according to fuel type and place of manufacture. domestic foreign gasoline 146 191 diesel 18 26 hybrid 51 79 Are place of manufacture and fuel type independent? If the two
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Let N be a random variable with mean E[N]=m, and Var(N)=v; let A1, A2,… be a sequence of i.i.d random variables, all independent of N, with mean 1 and variance 1; let B1,B2,… be another sequence of i.i.d. random variables, all
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