Answer:
a) Var (x) is larger
b)E(x)= 10 and E(y)= 2.5
Explanation:
a) Var (x) is larger because the number of students selected can be greater than 1 but Var(y) will always be less because the numbers of drivers chosen can be only one at a time.
b) The expected value of X and y can be computed by multiplying the numbers with their probabilities
x 10 20 30 40
P(x) 0.1 0.2 0.3 0.4
P (x= 10) = 10/ 10+20+30+40= 10/ 100= 0.1
E(x) = 10(0.1) +20(0.2) +30(0.3)+40(0.4)
E(x)= 1=2+3+4= 10
Now the expected value of y
y 1 2 3 4
P(y) 0.25 0.25 0.25 0.25
E(y)= 1(0.25) +2(0.25) +3(0.25)+4(0.25)
E(y)= 0.25 +0.5 +0.75 +1 = 2.5