Let X~N(0,1). Let Y=2X. Find the distribution of Y using the moment generating function technique.
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Let X~N(0,1). Let Y=2X. Find the distribution of Y using the moment generating
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- Find the marginal PDFs of X and Y.Let X₁ Bin(n1, p) and X₂ ~ Bin (n2, p). Find the distribution function of Y = X₁ + X₂. Assume X₁ L X₂. ~Help please: Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let Y = max{X1, X2, . . . , Xn}. Show that the PDF of Y has a Beta distribution.
- Solve: Let X ∼ Exp(λ), Y ∼ Exp(λ), and U ∼ Unif (0, 1). Find the distribution of U (X + Y ). Please don't handwriting solutionFigure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.The amount of water in a reservoir at the beginning of the day is a random variable X and theamount of water taken from the reservoir during the day is a random variable Y . The joint pdffor X and Y isf (x, y) ={1/200, 0 < y < x < 20;0, otherwise.Use the distribution function technique to find the pdf of the amount of water left in thereservoir at the end of the day
