The p.d.f of the binomial distribution random variable X with parameters n and p is f(x)...

The p.d.f of the binomial distribution random variable X with parameters
n and p is

f(x) =
n
x

p
x
(1 − p)
n−x x = 0, 1, 2, ..., n
0 Otherwise

Show that
a) Pn
x=0 f(x) = 1 [10 Marks]
b) the MGF of X is given by [(1 − p) + pet
]
n
. Hence or otherwise show
that E[X]=np and var(X)=np(1-p).

Solutions

Expert Solution

orchestra answered 1 year ago

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