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:
(4.256) 
(b) Derive the conditional pdfs fY|X(y|x) and fX|Y(x|y).
4.6 Repeat Problem 4.5 for (a)
(4.257)
and (b)
(4.258)
4.7 Two dice are tossed sequentially. ...
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