Let x be a binomial random variable with n 7 p 04 Find the

Let x be a binomial random variable with n = 7, p = 0.4. Find the following values.

(a) P(x=4)

(b) P(x 1)

(c)    P(x > 1)

(e)    

=

npq

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 4 ) = ( 7 4 ) * ( 0.4^4) * ( 1 - 0.4 )^3
= 0.1935
b)
P( X < = 1) = P(X=1) + P(X=0)
= ( 7 1 ) * 0.4^1 * ( 1- 0.4 ) ^6 + ( 7 0 ) * 0.4^0 * ( 1- 0.4 ) ^7   
= 0.1586
c)
P( X > 1) = 1 - P ( X <=1) = 1 -0.1586 = 0.8414
d)
stanadard devitaion = 7*0.4*0.6=1.68