PROBLEMS

Approximations of Random Variables

4.1 Show that the chi-square random variable with parameter N is Gaussian with parameters as .

4.2 Demonstrate that Student's t distribution with parameter r is approximately standard Gaussian for large r.

4.3 Show that the negative binomial distribution with parameters {n, p} is Poisson with parameter as .

4.4 Show that the gamma distribution with parameters is Gaussian with parameters as .

Joint, Marginal, and Conditional Distributions

4.5 (a) Find the marginal pdfs for the following joint pdf:

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(b) Derive the conditional pdfs fY|X(y|x) and fX|Y(x|y).

4.6 Repeat Problem 4.5 for (a)

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and (b)

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4.7 Two dice are tossed sequentially. ...

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