Consider two independent random variables X1 andX2 having the same Cauchy distributionf(x) = 1π(1 + x2)for − q < x < qFind the probability density of Y1 = X1 + X2 by usingTheorem 1 to determine the joint probability density ofX1 and Y1 and then integrating out x1. Also, identify thedistribution of Y1.

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A: Given that  Show that the probability density function of a negative binomial random variable equals…

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Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) &gt; 0.

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A: the probability mass function of random variable X isf(x)=8712x , x=1,2,3

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Q: 2. Let X be a random variable with density function f(x) = = √ (2x3 -8x2 +5x+6), 1<x<2, 0, elsewhere…

A: given function is f(x)=

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Q: value

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A: From the given information, fx1, x2=4X1(!-X2), 0&lt;X1&lt;1, 0&lt;X2&lt;1 Consider, P0&lt;X1&lt;1/3,…

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A: Give data:   0 1 2 P(Y) 0 11/73 18/73 14/73 43/73 1 10/73 8/73 0 18/73 2 12/73 0 0 12/73…

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A: Given:fx=cx2,                                   x≥10…

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Q: (a) Are X and Y statistically independent

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A: Given: There are three vectors.

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A: Let X ~ Bernoulli (p) .Then E(X) = p and V(X) = p (1-p).

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

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A: Step 1:Step 2:Step 3:Step 4:Final Answer (a). 77.667(b). 1492.955

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A: is a continuous random variable following a uniform distribution, that is .

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