Consider a single tossing of x unbiased coins:
a) Find the probability pX(x) of obtaining all heads; [2]
b) If x is regarded as a continuous variable in the range 0 ≤ x < ∞, show
that pX(x), regarded as a function of x and suitably scaled, determines
a probability distribution; [5]
c) Obtain a pdf of this distribution and calculate its cumulant generating
function; [5]
d) Hence or otherwise, show that the mean and variance are 1
ln 2 and
1
(ln 2)2 , respectively. [8]
e) Verify that the coefficient skewness for this distribution is γ3 = 2. [5]