Question

1. You’ve been given a lottery ticket with five mutually exclusive outcomes.

You could, with probability 1/20,000, win a grand prize valued at $8,000. You could also, with probability 1/20,000, win a major prize valued at $4,000. A minor prize valued at $150 can be won with probability 1/5,000; and a very minor prize of value of $3 can be won with probability 1/150. Finally, you could win nothing (valued at $0).

Find the mean and standard deviation of the value of your lottery ticket.

Answer 1

from given data:

x	P(x)	xP(x)	x2P(x)
8000	0.00005	0.400	3200.000
4000	0.00005	0.200	800.000
150	0.00020	0.030	4.500
3	0.00667	0.020	0.060
0	0.99303	0.000	0.000
	total	0.650	4004.560
	E(x) =μ=	ΣxP(x) =	0.6500
	E(x2) =	Σx2P(x) =	4004.5600
	Var(x)=σ2 =	E(x2)-(E(x))2=	4004.138
	std deviation=	σ= √σ2 =	63.2783

from above mean =$0.65

standard deviation =$63.28