Q2 Let (X₁, X₂) be jointly continuous with joint probability density function e-(²₁+²2), x₁ > 0, x₂ > 0 0 otherwise. f(x1, x2) = = Q2 (i.) Sketch(Shade) the support of (X1, X₂). Q2(ii.) Are X₁ and X₂ independent random variables? Justify your answer. Identify the random v X₂. 02(iii.) Let Y₁ = X₁ + X₂. Find the distribution of Y₁ using the distribution function method. i.e.

Q: 2) Let the joint probability function of X & Y be defined by Pxx (x, y) = x= 1,2 y = 1,2,3 Find…

A: The joint probability mass function of x and y is, P(x,y)=x+y21;x=1,2 and y=1,2,3 x=1, y=1…

Q: f(x) 0.5

A: It is an important part of statistics. It is widely used.

Q: k рех, у) хсу. y = 1,2,3 other - and the marginal probability function of Y P (Y) 6

A: Given PDF is p(x, y) = kx2y,x=1, 2,  y=1, 2, 30,otherwise

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Q: Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

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Q: C(4x – 2x2) 0 < x < 2 - f (x) = otherwise

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Q: Let the joint pdf of random variables X,Y be fx,y (x, y) = a(x + y)e-2-Y, for all æ > 0, y 2 0. Find…

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Q: The continuous random variable X has a probability density function (pdf) given by [1- x for 0 ).…

A: Given the continuous random variable X with probability density function: f(x) =  1 - 12X      for…

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A: Given, f(x) = 1/5  where x ∈ 38 f(x) is a p.d.f of x follows uniform distribution  x ~ U[ 3 , 8 ]

Q: * The waiting time T (in hours) between each SMS you receive is random with the density function.…

A:

Q: 2) Let the joint probability function of X & Y be defined by Pxy(x, y) = Find E(Y|X = 2). What is…

A: First we will create the joint probability distribution table for every value of x and y using the…