function fxy given by Suppose that X and Y have a joint probability density fxy(x, y) = Sce-2(x+y) if a > 0 and y> 0 otherwise Calculate the conditional density function fy|x=z(y).

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A: Given that : The joint density function is given.  By using marginal distribution of x we find the…

Q: a) Check whether X and Y are independent

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A: Given : The joint probability density function of X and Y is given by; fX,Yx,y=18x+y for…

Q: Let Continous Random Variables, X has the density function f(x) = [-5x +9 for 04x41 Lo else where…

A: f(x)=-5x+9 ; 0≤x≤1

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A: Given that, A and B have joint pdf: f(a,b)= 6(1-a-b)   ,   a+b&gt;1, a&gt;0,  b&gt;0

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Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

Q: What is the probability density of the area of the circle?

A: Given that  Radius = X, then the area of circle is  A = πX2

Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X² – 10X +…

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Q: et it be the probability density function. [ f(x2= n-x 2(1-2). ax Let it be Y = e x=0,1,2, So E(Y)…

A: Solution

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A: In question, Given that X has density function f(x). Then we'll find E(ex). The solution is below,

Q: is a probability - Find k such that f(x) = {kx(1 – x)² for 0 <x<1 %3D otherwise density function for…

A: The total probability must be 1. So,

Q: Is the function f(x) = 0, 0 < x < 1 3 - 1, 1<r < 3 otherwise a valid probability density function? O…

A: Any given function is a valid probability density function if it satisfies following two properties:…

Q: Let X be a continuous random variable with density function given by So a < 1 fx (x) = Find the…

A: The given density function is given by: fXx=0x&lt;1λxλ+1x≥1 Therefore the density function of Y=lnX…

Q: The continuous random variable X has a the following probability density function: p(x) = ) - {²…

A: From the given information, px=2λ1-xλ, x≤λ a) Graph: Excel procedure Enter x and p(x)in Excel…

Q: The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having…

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Q: Q1 Let (X₁, X₂) be jointly continuous with joint probability density function " f(x1, x₂) = x1 0 <…

A: Let  be jointly continuous with joint probability density function:

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A:

Q: random variables X and Y have a joint probability density function given by , y) = way, 0 < x < 3…

A:

Q: function fx,y given by Suppose that X and Y have a joint probability density - { fx.x (z,y) =…

A: given Pdf  f(x,y)=ce-2(x+y) x&gt;0, y&gt;0

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Q: Sketch the graph of the probability density function over the indicated interval. F(x) = 1/20, [0,…

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Q: *(a) Show that E(X) = aß and V(X) = aß². %3D #(b) Suppose that a = (pdf) of Y | and let Y= (X/ß)?.…

A: Given, Therefore, a.The E(X) and V(X) are given as follows:

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A: The distribution of y is given by:

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Q: c) A probability density function is of the form f(x) = Kexx € (-00,00). Estimate the value of K.

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Q: Let X be a continuous random variable with density function fx(x) = function of W=2-X, using the CDF…

A: