The purpose of this problem is to demonstrate the relationships among
the four
forms of convergence, i.e., almost surely, in probability, in mean
square and
in distribution. In each case, ([0; 1];B([0; 1]); P) is the underlying
probability space, with probability measure described by the uniform
pdf. For each of the following sequences of random variables,
determine the pmf of {Yn}, the senses in which the sequences
converges, and the random variable and pmf to which the sequence
converges.
a)
Yn(w) = 1 if n is odd and w < 1/2 or n is even and w > 1/2
      = 0 otherwise
b)
Yn(w) =  1 if w < 1/n
       = 0 otherwise
c)
Yn(w) = n if w< 1/n
      = 0 otherwise

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Request for Question Clarification by rbnn-ga on 04 Dec 2002 13:25 PST

What is "pmf"? Also by "[0;1]" I assume you mean the closed unit
interval, and by B([0;1]) I assume you mean borel sets on that
interfal.