Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always...

Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always the positive root.)

What is the P[X>=E[X]] ?

What is the E[Y] ?

what is the P[Y>=E[Y]]?

what is the PFD of f_Y(y)?

Solutions

Expert Solution

The PDF fX(x) of a Uniformly distributed random variable X, on (a,b) is fX(x) = 1/(b-a), for a<x<b

= 0, otherwise

The Cumulative Distribution Function, FX(x) = 0, for x≤a

= (x-a)/(b-a), for a<x<b

= 1, for x≥b

P(X≥a) = 1-P(X<a) = 1-FX(a) or P(X≥a) =

P[X≥E[X]] = 0.5

E[Y] = 4/3 = 1.3333

P[Y≥E[Y]] = 0.5556

The PDF of Y is fY(y) = y/2, 0<y<2

= 0, otherwise

orchestra answered 1 year ago

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