Question

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

(a)  ?=4,?=0.8
?=
?2=
?=

(b)  ?=5,?=0.3
?=
?2=
?=

(c)  ?=6,?=0.9
?=
?2=
?=

(d)  ?=5,?=0.9
?=
?2=
?=

Answer 1

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

?= np
?2= npq
?=sqrt(npq)

q = 1 - p

(a)  ?=4,?=0.8
?= 4*0.8 = 3.2
?2= 4*0.8*0.2 = 0.64
?= Sqrt(0.64) = 0.8

(b)  ?=5,?=0.3
?= 5*0.3 = 1.5
?2= 5*0.3*0.7 = 1.05
?= sqrt(1.05) = 1.024695

(c)  ?=6,?=0.9
?= 6*.9 = 5.4
?2= 6*.9*.1= 0.54
?= sqrt(0.54) = 0.734847

(d)  ?=5,?=0.9
?= 5*0.9 = 4.5
?2= 5*0.9*0.1 = 0.45
?= sqrt(0.45) = 0.67082