Question

Suppose X is a random variable taking on possible values 0,2,4 with respective probabilities .5, .3, and .2. Y is a random variable independent from X taking on possible values 1,3,5 with respective probabilities .2, .2, and .6. Use R to determine the following.

a) Find the expected value of Y.

b) Find the variance of Y.

c) Find the expected value of Y⁴ .

PLEASE SHOW ANSWER IN R SCRIPT

Answer 1

The R script is
X=c(0,2,4)
P1=c(0.5,0.3,0.2)
Y=c(1,3,5)
P2=c(0.2,0.2,0.6)
#Expected Value of Y
Ey=sum(Y*P2)
Ey
# Expected Value of Y is 3.8
#Variance of Y
Vy=sum((Y-Ey)^2*P2)
Vy
#Variance of Y is 2.56
# Expected value of Y^4
Ey4=sum(Y^4*P2)
Ey4
# Expected value of Y^4 is 391.4

The R Code is

X=c(0,2,4)

P1=c(0.5,0.3,0.2)

Y=c(1,3,5)

P2=c(0.2,0.2,0.6)

#Expected Value of Y

Ey=sum(Y*P2)

Ey

The Output of code is

>X=c(0,2,4)

>P1=c(0.5,0.3,0.2)

>Y=c(1,3,5)

>P2=c(0.2,0.2,0.6)

>#Expected Value of Y

>Ey=sum(Y*P2)

>Ey

[1] 3.8

>#Variance of Y

>Vy=sum((Y-Ey)^2*P2)

>Vy

[1] 2.56

># Expected value of Y^4

>Ey4=sum(Y^4*P2)

>Ey4

[1] 391.4