Question

Fiji tattslotto sells a lottery ticket for two dollars. Out of 10,000 tickets printed for this lottery, 1 ticket has a price of five thousand dollars, 5 tickets have a price of one thousand dollars each, 100 tickets have a price of $10 each and 1000 tickets contain a price of five dollar each. Let X be the r.v. that denotes the net amount a player wins in this lottery.

a write the probability of distribution of X.

b.Determine the mean of X.

Answer 1

Given,

X be the r.v. that denotes the net amount a player wins in the lottery.

Out of 10,000 tickets, 1 ticket has a price of $5000, so there is 1/10000 probability of getting price of five thousand dollars.

5 tickets have a price of $1000 each, so there is 5/10000 probability of getting price of one thousand dollars.

100 tickets have a price of $10 each, so there is 100/10000 probability of getting price of ten dollars.

And 1000 tickets contain a price of five dollar each, so there is 1000/10000 probability of getting price of five dollars.

This implies 10000 - (1+5+100+1000) = 8894 tickets contain no price, so there is 8894/10000 probability of getting no price.

So, the r.v. X take value 0, 5, 10, 1000 and 5000 with probability 8894/10000, 1000/10000, 100/10000, 5/10000 and 1/10000 respectively.

a) The probability distribution of X is a follows:

X	0	5	10	1000	5000
P(X=x)	0.8894	0.1	0.01	0.0005	0.0001

b) Mean of X is given by