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=0.7
μ=
σ2=
σ=

(b) n=3,p=0.7
μ=
σ2=
σ=

(c) n=5,p=0.4
μ=
σ2=
σ=

(d) n=5,p=0.8
μ=
σ2=
σ=

Answer 1

Solution(a)

Mean of the bionomial distribution = (n*p)= (4*0.7)=2.8

Varinace of bionomial distribution = n*p*q = 4*0.7*0.3 = 0.84

Standard deviation of bionomial distribution = sqrt(variance)= sqrt(0.84)= 0.9165

Solution(b)

Mean = 3*0.7 = 2.1

Variance = 3*0.7*0.3=0.63

Standard deviation = sqrt(0.63)= 0.7937

Solution(c)

Mean = 5*0.4=2

Varinace = 5*0.4*0.6 = 1.2

Standard deviation = sqrt(1.2)= 0.9554

Solution(d)

Mean = 5*0.8= 4

Varinace = 5*0.8*0.2= 0.8

Standard deviation = sqrt(0.8)= 0.8944