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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
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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