The following table lists the probability distribution for cash prizes in a lottery conducted at?

Question

The following table lists the probability distribution for cash prizes in a lottery conducted at
Lawson’s Department Store.

Prize ($) Probability
0 .45
10 .30
100 .20
500 .05

If you buy a single ticket, what is the probability that you win:
a. Exactly $100? b. At least $10? c. No more than $100?
d. Compute the mean, variance, and standard deviation of this distribution.

Answer 1

a) 0.20 (given)
b) 0.30 + 0.20 + 0.05 = 0.55; or 1 - 0.45 = 0.55.
c) 0.45 + 0.30 + 0.20 = 0.95; or 1 - 0.05 = 0.95.
d) Mean is 0(0.45) + 10(0.30) + 100(0.20) + 500(0.05) = $51.
Variance is 0.45(0) + 0.30(100) + 0.20(10000) + 0.05(250000) - 51^2 = 11929
Standard deviation = √11929 = $109 (nearest dollar).

Answer 2

1(.11)+2(.18)+(3(.21+4(.16)+5(.18)+6(.09...