A random variable X has a binomial distribution with paramet

A random variable X has a binomial distribution with parameters n,p,q. Also the (meoo ) = 10.56 and (sigma ) ^2 = 7.1808.
Find
a) n,p,q.
b) Find p (X>=3)
c) Find E ( 3x^2) and Var (3x).

A random variable X has a binomial distribution with parameters n,p,q. Also the (meoo ) = 10.56 and (sigma ) ^2 = 7.1808. Find a) n,p,q. b) Find p (X>=3) c) Find E ( 3x^2) and Var (3x).

Solution

In a binomial variable

sigma^2 = npq and mean = np

a) npq = 7.1808

b) For finding prob let us find p and q first

np = 10.56 Hence q = 0.68 and p =0.32 and n =33

P(X>=3) = 0.9996

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c) E(3x^2) = 9E(x^2) = 9(varx+mean^2) = 9(70.2972+111.5136) = 1636.2972

Var(3x) = 9 var(x) = 9(7.8108)= 70.2972