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Suppose you have two fair dice, each with 6 faces. • One die is coloured blue and has the following faces: {1, 1, 1, 2, 2, 3}. • The other die is coloured red, and has the following faces {1,1,2, 2, 3, 3}. You found in Term Test 3 that the probability distributions for these dice are 1/2 m = 1 PR(M) = 3 1 for all n e {1,2, 3}, PB(m) 1/3 m = 2 1/6 m = 3 where PB corresponds to the blue die, and pR corresponds to the red die. Consider the dice defined in the box at the top of the page. (i) die. You both pay $1 and roll your die. Whoever rolls the higher number wins the money. If both You're playing a game against Alexey. You have the blue die and Alexey has the red dice are the same, both players get their money back. What is the expected value of your winnings if you play one round of this game? (Note that if you pay $1 to play the game, and win $2, you have won $1). (ii) is the expected value of your winnings. You and Alexey play another round of the same game, but you now switch dice. What

Suppose you have two fair dice, each with 6 faces. • One die is coloured blue and has the following faces: {1, 1, 1, 2, 2, 3}. • The other die is coloured red, and has the following faces {1,1,2, 2, 3, 3}. You found in Term Test 3 that the probability distributions for these dice are 1/2 m = 1 PR(M) = 3 1 for all n e {1,2, 3}, PB(m) 1/3 m = 2 1/6 m = 3 where PB corresponds to the blue die, and pR corresponds to the red die. Consider the dice defined in the box at the top of the page. (i) die. You both pay $1 and roll your die. Whoever rolls the higher number wins the money. If both You're playing a game against Alexey. You have the blue die and Alexey has the red dice are the same, both players get their money back. What is the expected value of your winnings if you play one round of this game? (Note that if you pay $1 to play the game, and win $2, you have won $1). (ii) is the expected value of your winnings. You and Alexey play another round of the same game, but you now switch dice. What

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Suppose you have two fair dice, each with 6 faces. • One die is coloured blue and has the following faces: {1,1,1,2, 2, 3}. • The other die is coloured red, and has the following faces {1,1, 2, 2, 3, 3}. You found in Term Test 3 that the probability distributions for these dice are 1/2 m = 1 рв(т) — { 1/3 т%3D2 PR(n) 1 for all n e {1,2, 3}, 3 1/6 т — 3 where PB corresponds to the blue die, and PR Corresponds to the red die. Consider the dice defined in the box at the top of the page. (i) You're playing a game against Alexey. You have the blue die and Alexey has the red die. You both pay $1 and roll your die. Whoever rolls the higher number wins the money. If both dice are the same, both players get their money back. What is the expected value of your winnings if you play one round of this game? (Note that if you pay $1 to play the game, and win $2, you have won $1). (ii) is the expected value of your winnings. You and Alexey play another round of the same game, but you now switch dice. What
Transcribed Image Text:Suppose you have two fair dice, each with 6 faces. • One die is coloured blue and has the following faces: {1,1,1,2, 2, 3}. • The other die is coloured red, and has the following faces {1,1, 2, 2, 3, 3}. You found in Term Test 3 that the probability distributions for these dice are 1/2 m = 1 рв(т) — { 1/3 т%3D2 PR(n) 1 for all n e {1,2, 3}, 3 1/6 т — 3 where PB corresponds to the blue die, and PR Corresponds to the red die. Consider the dice defined in the box at the top of the page. (i) You're playing a game against Alexey. You have the blue die and Alexey has the red die. You both pay $1 and roll your die. Whoever rolls the higher number wins the money. If both dice are the same, both players get their money back. What is the expected value of your winnings if you play one round of this game? (Note that if you pay $1 to play the game, and win $2, you have won $1). (ii) is the expected value of your winnings. You and Alexey play another round of the same game, but you now switch dice. What
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