3. Determine the constant a so that f(x) is a valid density function. - f(x) = {a(3 — x²), a) 0.3333 b) 0.3889 c) 0.4000 d) 0.1875 -1 ≤ x ≤ 1, elsewhere.
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Ans#- Given, f(x) is valid density function
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- Definition: A function ƒ : R → R is said to be periodic with period L if f(x + L) = f(x) for every x E R. Consider the space P of continuous periodic functions on R with period 27 such that π [** f(x) dx = 0 ASuppose X has PDF fx(x) = x/2 for 0 < x < 2 and 0 otherwise. (a) Find E[X] for n = = 0, 1, 2,...,. (b) Find the density function of Y differentiating. = X(2X) by computing P(Y ≥ y) and then3. Find all continuous positive functions f (if any) defined on (0, 1] so that | (=) dz = 1. "E) sin(rz) dz S() sin (#) dz = . %3D Activate Windows Go to Settings to activate Windows. where a is a given real nuomber.
- Please write each step.For X and Y continuous, P(X = x|Y = Y) = O 1 O 1/2 P(X = x) P(Y = y)1.5 Solve the below problem: Let Y, and Y, have a joint density function given by f(n. Y2) = $3y1 0< y2 < yı <1 lo, elsewhere. The marginal density function for Y, is f(v2) =(1 – y3), 0 < y2 < 1. Find the marginal density function of Y1. (NB: Show all your calculations)
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