Let X be a random variable defined by the pdf fx(x) = x2 [u(x) – u(x - 1)] + a)(x – 2), where u(x) is the unit step func

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Let X Be A Random Variable Defined By The Pdf Fx X X2 U X U X 1 A X 2 Where U X Is The Unit Step Func 1 (165.52 KiB) Viewed 27 times

Let X be a random variable defined by the pdf fx(x) = x2 [u(x) – u(x - 1)] + a)(x – 2), where u(x) is the unit step function which is equal to 1 when x > 0 and 0 otherwise, and 8(x) is the impulse function (Dirac delta function) which is the (generalized) derivative of u(x). a) Find a, E[X] and Var[X] b) Define the event W = {X > 0.5}. Find P[X 5 xW] for all x € R. We shall define Fx\w(x) = P[X < x\W) the conditional CDF given the event W. Find a nonnegative function f :R + R that satisfies ſs(t)dt = Fx\w(a) va er We can call this a conditional PDF given W. Find the set of all x E R over which your function f satisfies f(x) > 0. This is often called the “support” of the function.