Question

Random variable X determines the range of voltage values at the output of an electronic module,...

Random variable X determines the range of voltage values at the output of an electronic module, and is drawn from probability density function fX(x) = (1/x^2) * u(x − 1). Random variable Y is the actual voltage observed and depends on X in the following way: if X takes the value x then Y is uniformly distributed in the range [−x, x].

Find

a) The joint density fXY (x, y).

b) The marginal density of the observed voltage fY (y).

c) Given observation of the voltage you would like to deduce as much as possible on the unobserved range X. Find the conditional density f X|Y (x|y).

Math   Statistics-And-Probability   
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Answer #1

The probability density function of X is .

The conditional  probability density function of Y is

a) The joint PDF is

b) The marginal PDF is

For

For

Thus the marginal PDF is

c) The conditional PDF is

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