Question

If x is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

(a)  n=3,p=0.9
μ=
σ^2=
σ=

(b)  n=6,p=0.1
μ=
σ^2=
σ=

(c)  n=4,p=0.6
μ=
σ^2=
σ=

(d)  n=5,p=0.8
μ=
σ^2=
σ=

Answer 1

solution

(a)

p=0.9

n=3

q=1 -0.9 =0.1

Using binomial distribution,

Mean = = n * p = 3* 0.9 = 2.7

variance=n * p * q = 3 *0.9 *0.1= 0.27

Standard deviation = = n * p * q = 3 *0.9 * 0.1= 0.5196

(B)

p=0.1

n=6

q=1 -0.1 =0.9

Using binomial distribution,

Mean = = n * p = 6* 0.1 = 0.6

variance=n * p * q = 6 *0.1 *0.9= 0.54

Standard deviation = = n * p * q = 6*0.9 * 0.1= 0.7348

(C)

p=0.6

n=4

q=1 -0.6=0.4

Using binomial distribution,

Mean = = n * p = 4* 0.6 = 2.4

variance=n * p * q = 4 *0.6 *0.4= 0.96

Standard deviation = = n * p * q = 4*0.6 * 0.4= 0.9798

(d)

p=0.8

n=5

q=1 -0.8=0.2

Using binomial distribution,

Mean = = n * p = 5* 0.8 = 4

variance=n * p * q = 5 *0.8 *0.2= 0.8

Standard deviation = = n * p * q = 5*0.8 * 0.2= 0.8944