Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function: Р(ху) х -1 1/3 1/3 1/3 Use the definition of independence on page 141 to show that X and Y are not independent (in fact Y = |X], so Y is actually a function of X). b. a. Show that X and Y are uncorrelated.

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A: Solution: From the given information, the joint probability for X and Y is

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A: Given that:

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A: Given Joint PMF OF X and Y are as follows

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A: given that

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A:

Q: Consider a discrete random variable with the following probability mass function. 4-x x = 1,2, 3…

A: Given,f(x)=4-x6   ;  x=1,2,30          ;   else X 1 2 3 f(x)    (P(X)) 3/6 2/6 1/6

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A:

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A:

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A: Solution We have given x P(X=x) -2 0.05 0 0.25 1 0.25 2 0.35 5 0.01

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A: Chebyshev's inequality is: P(|X-μ|≥kσ)≤1/k2