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X has the uniform distribution [0,1] Put Y=2x + 5. If f(x) is the
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- Consider the joint PDF f(x,y)=4xy for 0<x<1 and 0<y<1. (a) Are X and Y independent?(b) Find both marginal distributions. (c) Find both conditional distributions.Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?Let f(x) = ½ , -1 < x < 1 0 otherwise be a pdf of the random variable X. Find the distribution function and the pdf of Y= X2
- Find the pdf of e^x in terms of the pdf of X, base the answer to the case where X is uniformly distributed between 0 and 1Let X be a continuous random variable with a pdf f(x) = { kx5 0≤x≤1, 0 elsewhere Determine the value of k.If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
- Let X~N(0,1). Let Y=2X. Find the distribution of Y using the moment generating function technique.a. What is the joint marginal PDF of X and Z?b. What is [P 0 <= Y <= 3/2 | X = 1/3 Z = 5/2]?Let x and y be joint continuous random variable with joint pdf f XY (x, y) = {cx+ 1, x, y ≥ 0, x + y < 10, otherwise1. Find the constant c.2. Find the marginal PDF’S fX (x) and fY (y)3. Find P(Y<2X2)