Question

5. Let X represents the number of computers in an Australian household, for those that own a computer.



a. Find and interpret the expected number of computers in a randomly selected Australian
household. (2 marks)
b. What is the probability that a randomly selected Australian household will have more than 2
computers? (1 mark)
c. Find V (4X +2). (1 mark)
d. Find E(30X + 20]. (1 mark)

Answer 1

$\begin{matrix} x & 1 & 2 & 3 & 4 & 5 \\ p(x) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10 \end{matrix}$

a) . The expected number of computers in a randomly selected Australian household

$=E(X)=1(0.25)+2(0.33)+3(0.17)+4(0.15)+5(0.10) =2.52$

The expexted number of computers in an Australian household, for those that own a computer is

2.52computers.

b) . The probability that a randomly selected Australian household will have more than 2 computers is

$P(X>2)=0.17+0.15+0.10=0.42$

c) .$V(X)=(1-2.52)^2(0.25)+(2-2.52)^2(0.33) +(3-2.52)^2(0.17)+(4-2.52)^2(0.15)+(3−2.52) +(5-2.52)^2(0.10)=1.6496$

$V(4X+2)=4^2\cdot V(X)=16\cdot1.6496=26.3936$

d) .$E(30X+20)=30E(X)+20=30⋅2.52+20=95.6$