Class summary:
Monday, 4/28
I began the final topic in this class, sums of independent random
variables. The density of a sum of two independent
continuous r.v.'s can be obtained by the so-called "convolution
formula" - given on p. 372 in Pitman.
I discussed this formula, its motivation and
proof (which proceeds via the c.d.f. and is based on the Fundamental Theorem
of Calculus),
and I illustrated it by working out two examples:
the sum of two independent exponential r.v.'s, and the sum of two
independent uniform r.v.'s.
Reading Guide to Chapter 5.
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