and , respectively. Assume that X₁ and X₂ are independent of each other. 3 Find i) The joint density function of X₁ and X₂. ii) P(X₁ >1, X₂ > 1)

Q: 5)? a What is P(Y₁ b What is P(Y₁+ Y₂ < 3)?

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Q: Let X and Y have joint density fx,y(x, y) = (6 - x - y) I(0,2)(x) I(2,4) (y). a. Find Var[Y| X = x].…

A: The joint distribution of X and Y is as follows: fX,Y(x,y)=18(6-x-y); 0&lt;x&lt;2, 2&lt;y&lt;4 The…

Q: 3. Determine the constant a so that f(x) is a valid density function. - f(x) = {a(3 — x²), a) 0.3333…

A: Ans#- Given, f(x) is valid density function           f(x) = a(3 - x2)-1 ≤x≤10otherwise…

Q: Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table.…

A: The joint probability distribution of X and Y is f(x,y)   1       2       31           1/4    1/4…

Q: The value of c

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Q: The time to failure in hours of an important piece of electronic equipment used in a manufactured…

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Q: Assuming that X and Y have joint distribution f (x, y) = cx for -x < y < x, 0 < x < 1, and f(x, y) =…

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Q: Let X and Y have the joint density function 1 f(x, y): x > 1, y > 1. Let U = XY and V = 3X/Y. (a)…

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Q: a) Are Y1 and Y2 independent? b) Find V(Y1 – 2Y2), if we know that E(Y,) = E(Y 2) =}.

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Q: ... If the joint pdf of (X,Y) is f (x, y) = 6e-2x-3y 9 , x ≥, y0 ≥, find0 the conditional density of…

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Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 < x, y < 1, x+y<1 otherwise…

A: From the given information, fx,y=651+x+y, 0≤x,y≤1, x+y≤1 g) Consider, fx=∫yfx,ydy…

Q: 2. Let f(x₁, X2, X3, X4) be the joint density function of (X₁, X2, X3, X 4). Then the joint density…

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Q: Assuming that X and Y have joint distribution f(x,y) = cx for -x < y < x, 0 < x< 1, and f(x, y) = 0…

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Q: Let Y possess a density function f (y) = c(2 − y),                        0 ≤ y ≤ 2,        0,…

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Q: owing joint dens f(y1, y2) : 0<y1<1, 0, otherwise a) Find P(Y1<¥2). b) Find P(Y1<¥2 = ).

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Q: Is the function defined as follows a density function? fx (x) = 0 for x < 2 (3 + 2x) 18 for 2 <x< 4…

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Q: Let and Y have the joint density function 2, 0<x<1; 0 <y<x, f(x,y)= 0, Otherwise. Calculate E(XY).

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Q: Let Y have the density function given by 0 <y< 2 f(2) = {-cy", (-су?, 0, elsewhere a. ) Find c. b. )…

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Q: fxy(г,у) — 8гу for (z,y) € A

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Q: Let Y₁ and Y₂ have joint density f(y₁, y2) = 3c(1 - y₂) on 0 ≤ y₁ ≤ 2 and 0 ≤ y₂ ≤ 1. What is the…

A: Given, the joint density of Y1 and Y2 is

Q: Let X and Y be continuous random variables with joint density function { if x E R, y > 0 f(x, y) =…

A: # Joint pdf of random variable x and y is given f(x,y)=e^-(y+x^2)/sqrt(π) : x from real number and…

Q: The density function of X is:  f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

A: The density function of X is: f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

Q: Find the conditional density of X, given Y = y, and that of Y , given X = x. Make sure to define the…

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Q: Let f(x) is density function then

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Q: Consider the joint density function 1, f(x, y) = 10, Compute the correlation coefficient pxy. x>2,…

A: The given joint pdf of (X,Y) is as follows,  f(x,y)=16yx3 ,2≤x,0&lt;y&lt;1

Q: Let X and Y have the joint probability density function ¹, for 0<x<2, 0<y<1 otherwise 0, Find the…

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