1 with probability 1=2
1 with probability 1=2
Let Y = SX.
Answer the following questions:
(a) Let y be a real number. Fill in the gaps indicated with : : : in the following identity:
P(Y y) = P(SX yj : : :)P(: : + P(SX yj : : :)P(: : :):
Name the theorem that is the basis for the identity above. [2 marks]
(b) Find the cdf of Y . Show your working. [6 marks]
(c) Find the pdf of Y . Show your working. [2 marks]
(d) Let V =
p
X. Find the pdf of V , remembering to include the range of values of v for
which your answer is valid. [5 marks]
[Total: 15 marks]
