If x is a binomial random variable compute the mean the stan

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=0.1
?=
? 2 =
?=

(b) n=3,p=0.2
?=
? 2 =
?=

(c) n=5,p=0.3
?=
? 2 =
?=

(d) n=4,p=0.5
?=
? 2 =
?=

Solution

For a binomial variable, mean= np and variance= npq, standard deviation = sqrt(npq)

a) n=4, p=0.1

mean= np= 0.4, variance= npq= 4*0.1*0.9= 0.36, std dev= sqrt(0.36)=0.6

b) n=3, p=0.2

mean= np= 0.6, variance= npq= 3*0.2*0.8=0.48, std dev= sqrt(0.48)=0.6928

c) n=5, p=0.3

mean= np= 1.5, variance= npq= 1.5*0.7=1.05 , std dev= sqrt(1.05)=1.024

d) n=4, p=0.5

mean= np= 2, variance= npq= 2*0.5=1, std dev= sqrt(1)= 1