Problem 4. Gaussian Random Variables

  1. Problem 4. Gaussian Random VariablesLet X be a standard normal random variable. Let Y be a continuous random variable such that
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  2. A zero-mean Gaussian random process has an auto-correlation functionR_XX (τ)={■(13[1-(|τ|⁄6)] |τ|≤6@0 elsewhere)┤
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  3. In this problem, you may find it useful to recall the following fact about Poisson random variables. Let X and Y be two
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  4. Problem 2. Continuous Random Variables2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous
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  5. Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variablesY1 =X1−X3,
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  6. Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variablesY1 =X1−X3,
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  7. Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variablesY1 =X1−X3,
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  8. Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variablesY1 =X1−X3,
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  9. Convergence in distributionLet Tn be a sequence of random variables that converges to N(0,1) in distribution. Call Y = 2*Tn + 1
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  10. You observe k i.i.d. copies of the discrete uniform random variable Xi, which takes values 1 through n with equal probability.De
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