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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

What is the expected value of a game that works as follows: I flip a coin and if tails pay you ₹ 2; if heads pay you ₹ 1. In either case, I also pay you ₹ 50 - Business Mathematics and Statistics

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Question

What is the expected value of a game that works as follows: I flip a coin and if tails pay you ₹ 2; if heads pay you ₹ 1. In either case, I also pay you ₹ 0.50

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Solution

Let x be the remain variable denoting the amount paying for a game of flip coin then x and takes 2 and 1

P(X = 2) = `1/2` (getting a head)

P(X = 1) = `1/2` (getting a tail)

Hence the probability of X is

X 2 1
P(X = x) `1/2` `1/2`

Expected value E(X) = `sum_x "P"(x)`

= `(2)(1/2) + 1(1/2)`

= `1 + 1/2`

= `3/2`

Since I pay you ₹ 50 in either case

E(X) = 50 × `3/2` = ₹ 75

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Mathematical Expectation
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Chapter 6: Random Variable and Mathematical expectation - Miscellaneous problems [Page 144]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 6 Random Variable and Mathematical expectation
Miscellaneous problems | Q 7 | Page 144

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