SOLVED: Question 4: Continuous Joint Distribution(20 marks)Let the random variables X and Y have the joint PDFf(z,y) = axye, 1 < z < 2, 0 < y < 0, otherwise.(i) Find the constant a0 that f(z,y) is a joint probability density function. (marks)(ii) Find P(X < 2, Y < 1). (marks)(iii) Find the marginal probability density function fy(y) for Y. (marks)(iv) Find the conditional probability density function fxiy-y(z). Hence write an integral formula for the expectation (X). You do not need to evaluate
SOLVED: Question 4: Continuous Joint Distribution(20 marks)Let th…
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SOLVED:The joint distribution of the continuous random variables X, Y, and Z is constant over the region x^2 y^2 ≤1 0 < z < 4. Determine the following: (a) P(X^2 Y^2 ≤0.5) (b) P(X^2 Y^2 ≤0.5, Z < 2) (c) Joint conditional probability density function of X and Y given that Z=1 (d) Marginal probability density function of X (e) Conditional mean of Z given that X=0 and Y=0 (f) Conditional mean of Z given that X=x and Y=y
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SOLVED:Probability A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties. (a) f(x, y) ≥0 for all (x, y) (b) ∫-∞^∞ ∫-∞^∞ f(x, y) d A=1 (c) P[(x, y) ∈R]=∫R ∫f(x, y) d A Show that the function is a joint density function and find the required probability. f(x, y)={ (1)/(27)(9-x-y), 0 ≤ x ≤ 3,3 ≤ y ≤ 6 0, elsewhere. P(0 ≤x ≤1,4 ≤y ≤6)
SOLVED:Probability A joint density function of the continuous rando…
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