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=4,p=0.4n=4,p=0.4
μ=
σ2=
σ=

(b)  n=3,p=0.2n=3,p=0.2
μ=
σ2=
σ=

(c)  n=3,p=0.6n=3,p=0.6
μ=
σ2=
σ=

(d)  n=6,p=0.7n=6,p=0.7
μ=
σ2=
σ=

Answer 1

solution

p = 0.4

q = 1 - 0.4 = 0.6

n =4

Mean = = n * p = 4 *0.4=1.6

variance = σ2 =n * p * q =  4*0.4*0.6=0.96

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

(b)p = 0.2

q = 1 - 0.2 = 0.8

n =3

Mean = = n * p = 3 *0.2=0.6

variance = σ2 =n * p * q = 3*0.2*0.8=0.48

Standard deviation = = n * p * q =   3*0.2*0.8=0.6928

(c)p = 0.6

q = 1 - 0.6 = 0.4

n =3

Mean = = n * p = 3 *0.6=1.8

variance = σ2 =n * p * q = 3*0.6*0.4=0.72

Standard deviation = = n * p * q =   3*0.6*0.4=0.8485

(d) p = 0.7

q = 1 - 0.7 = 0.3

n =6

Mean = = n * p = 6 *0.7=4.2

variance = σ2 =n * p * q = 6*0.7*0.3=1.26

Standard deviation = = n * p * q =   6*0.7*0.3=1.1225