Question

SEON BACK CES Chapter 05, Section 5.3, Problem 024 An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 500 tickets contain a prize ot $3 each, 125 tickets have a prize of $10 each, 2 tickets have a for this 000 each, and 1 ticket has a prze of $500. Let x be the random variable that denotes the net a playing this letery. toplayer wins by write the probability distribution of X. Enter the exact answers. Enter your answers for x in increasing order. P (x) Determine the mean and standard deviation of x Round your answers to two decimal places. On average, the players who play this game are expected to Click if you would like to Show Work for this question: en Show per ticket with a standard deviation or $ A Rights Reserved. A Division of

Answer 1

cost of lottery ticket = $2 500 tickets have rightarrow $5 each 125 tickets have rightarrow $10 each 2 tickets have prize of rightarrow $1000 each 1 ticket rightarrow $ 5000 Total tickets = 10,000(given) 10,000 - 628 = 9372 tickets 9372 tickets have rightarrow $0 prize money As 500 + 125 + 2 + 1 = 628 x denotes net prize won by by player x = $5 =$2: $10 $2 $1000 $2: $5000 $2x = $3;$8;$998;$4998 can take values rightdoublearrow 3 times 0.05 + 8 times 0.0125 + 998 times 0.0002 + 4998 times 0.0001 - 2 times 0.9372 \r\n rightdoublearrow E[x] = mu_x = -0.925 E[x^2] - [E[x])^2 = var(x) = x E[x^2] = summation^5_i = 1 x^2_i p(x_i) E[x^2] = g times 0.05 + 64 times 0.0125 + [998)^2 times 0.0002 + E[x^2] = 2702.2 [E[x]]^2 = 0.855625 E[x]^2 - [E[px])^2 = 2701.344375 = sigma x = Var(x) squareroot sigma x = squareroot var (x) = SD(x) SD(x) = squareroot 2701.344375 = 51.974458872 SD(x) = 51.97