A microscopic particle cannon fires spherical particles of radius R, which is a continuous random variable...
A microscopic particle cannon fires spherical particles of radius R, which is a continuous random variable with the PDF given by
fR(r) := ( ar + b r ∈ [1, 2] , and 0 else
It is further given that fR(2) = 1/2 .
(a). Find a and b.
(b) Let S = 4πR^2 be the surface area of a particle. Find E(S), the mean surface area.
(c). Let V = 4/3 πR^3 be the volume of a particle. Find fv (u) and E(V )
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A microscopic particle cannon fires spherical particles of
radius R, which is a continuous random variable...
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is expo...
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
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P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
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