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Example 19 : A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he gets Rs. 10, otherwise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable ?

Example 19 : A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he gets Rs. 10, otherwise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable ?

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LTE LMM 84% 1 10:02 AM KB/s LTE books.google.co.in/books? 2 Search Images Maps Play YouTube News Gmail Drive More - sumit4943@gmail.com - * Вooks Add to my library Write review Page 64 - > Result 1 of 1 for A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he BUY EBOOK - 309.75 gets Rs. 10 other wise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable? Clear search X 1 Get this book in print ▼ p(x) 3 Find (i) E(X) (ii) E(X') (iii) E[(2X + 1)*] ***** Engineering Mathematios 1 Review Write review Copyrighter Engineering Mathematics Volume - III (Statistical and Numerical Methods .. By lyenger T.K.V./ Gandhi, Krishna B./ Ranganatham S. & Prasad M.V.S.S.N. 64 Engineering Mathematics - III (Statistical & Numerical Methods) A player wins if he gets Go Solution : About this book 1 ++ 1 + 3 + 3 = 11 (i) E(X) = P,X, = (- 3) + 6 3 • My library • My History (ii) E(X) = P,x = (- 3)? ) + «6}³ . + (9³ . i=l Books on Google Play 36 81 93 %3D Terms of Service 6. 2 3 2 (iii) E[(2X + 1)] = E(4X + 4X + 1) = 4E(X) + 4E(X) + E(1) Pages displayed by permission of S. Chand Publishing. Copyright. 93 11 +4 418 + 1 = 2 = 4 = 209 Example 19: A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he gets Rs. 10, otherwise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable ? Solution : Range of X = {- 15, 10, 50} Since there are six numbers in a die, out of these 5 is only one number, the probability of getting Rs. 50 is 1 P(X = 50) = Similarly, the probability of getting two numbers (2 or 4) to win Rs. 10 is P(X = 10) = 6 3 The probability of getting three numbers (1 or 3 or 6) to loose Rs. 15 is P(X = - 15) = Discrete probability distribution is X = x - 15 10 50 1 1 P(X)= p(x) 3 25 Expected value of the game = E(X)=Ex;p (x,) =(-15)+10.+50.= Rs. 6. Game is favourable to the player since E > 0. Example 20 : A player tosses 3 fair coins. He wins Rs. 500 if 3 heads appear, Rs. 300 if 2 heads appear, Rs. 100 if 1 head occurs. On the other hand, he loses Rs. 1500 if 3 tails occur. Find the expected gain of the player. Solution: Let X denote the gain. Then the range of X is {- 1500, 100, 300, 500} The sample space S=n(s) = 23 = 8 %3D{HНН, ННТ, нтН, HT, THH, TH, TTH, TTT; Copyrighted Random Variables & Distribution Functions 65 1 The probability of all 3 heads (getting Rs. 500) = P(X = 3) = 8 3 The probability of getting 2 heads (getting Rs. 300) = P(X = 2) = 8 The probability of getting one head (getting Rs. 100) = P(X = 1) = 1 Le --:-- :1- 1---:-- D- TLJ
Transcribed Image Text:LTE LMM 84% 1 10:02 AM KB/s LTE books.google.co.in/books? 2 Search Images Maps Play YouTube News Gmail Drive More - sumit4943@gmail.com - * Вooks Add to my library Write review Page 64 - > Result 1 of 1 for A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he BUY EBOOK - 309.75 gets Rs. 10 other wise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable? Clear search X 1 Get this book in print ▼ p(x) 3 Find (i) E(X) (ii) E(X') (iii) E[(2X + 1)*] ***** Engineering Mathematios 1 Review Write review Copyrighter Engineering Mathematics Volume - III (Statistical and Numerical Methods .. By lyenger T.K.V./ Gandhi, Krishna B./ Ranganatham S. & Prasad M.V.S.S.N. 64 Engineering Mathematics - III (Statistical & Numerical Methods) A player wins if he gets Go Solution : About this book 1 ++ 1 + 3 + 3 = 11 (i) E(X) = P,X, = (- 3) + 6 3 • My library • My History (ii) E(X) = P,x = (- 3)? ) + «6}³ . + (9³ . i=l Books on Google Play 36 81 93 %3D Terms of Service 6. 2 3 2 (iii) E[(2X + 1)] = E(4X + 4X + 1) = 4E(X) + 4E(X) + E(1) Pages displayed by permission of S. Chand Publishing. Copyright. 93 11 +4 418 + 1 = 2 = 4 = 209 Example 19: A player wins if he gets 5 on a single throw of a die, he loses if he gets 2 or 4. If he wins, he gets Rs. 50, if he loses he gets Rs. 10, otherwise he has to pay Rs. 15. Find the value of the game to the player. Is it favourable ? Solution : Range of X = {- 15, 10, 50} Since there are six numbers in a die, out of these 5 is only one number, the probability of getting Rs. 50 is 1 P(X = 50) = Similarly, the probability of getting two numbers (2 or 4) to win Rs. 10 is P(X = 10) = 6 3 The probability of getting three numbers (1 or 3 or 6) to loose Rs. 15 is P(X = - 15) = Discrete probability distribution is X = x - 15 10 50 1 1 P(X)= p(x) 3 25 Expected value of the game = E(X)=Ex;p (x,) =(-15)+10.+50.= Rs. 6. Game is favourable to the player since E > 0. Example 20 : A player tosses 3 fair coins. He wins Rs. 500 if 3 heads appear, Rs. 300 if 2 heads appear, Rs. 100 if 1 head occurs. On the other hand, he loses Rs. 1500 if 3 tails occur. Find the expected gain of the player. Solution: Let X denote the gain. Then the range of X is {- 1500, 100, 300, 500} The sample space S=n(s) = 23 = 8 %3D{HНН, ННТ, нтН, HT, THH, TH, TTH, TTT; Copyrighted Random Variables & Distribution Functions 65 1 The probability of all 3 heads (getting Rs. 500) = P(X = 3) = 8 3 The probability of getting 2 heads (getting Rs. 300) = P(X = 2) = 8 The probability of getting one head (getting Rs. 100) = P(X = 1) = 1 Le --:-- :1- 1---:-- D- TLJ
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