Suppose X and Y are random variables with the given joint density function. f(x, y): {0.1e-(0.5 if x ≥ 0, y 20 otherwise 0.1e-(0.5x+0.2y) (a) Is f a joint density function? OYes No (b) Find P(Y 23). (Round your answer to four decimal places.)

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A: As per the guideline, 3 subparts can be answered at once. please repost remaining.

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A: The PDF of X and Y is given as:Also, the given transformation is:U=9XYandV=10X

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A: 1. From the given information, fx,y=1x2y2, x&gt;1, y&gt;1 Let U=6XY, V=7X V=7XV7=X And…

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A: Provided information is, fxx=12+14x       -2≤x≤0=12-14x       0≤x≤2=0                    elsewhere A…

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A: Given: fy1, y2=6y12y2,       0≤y1≤y2, y1+y2≤20,               Otherwise Required P(Y2 &lt; 1.1 | Y1…

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Q: Thank you!

A: There is no common region; therefore the probability is equal to 0.

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A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

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Q: The density function of X random variable is given below. 0<z<2, f:(z) = otherwise. Y random…

A: If x=0, then y= 3x2-2x=3(0)2-2(0)=0 If x=2, then y= 3x2-2x=3(2)2-2(2)=8   So, 0≤y≤8

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A: given;X be a continuous random variable with density function:f(x)=cx0≤x≤20otherwise