individual plays a game of tossing a coin

bidyut narzary

bidyut narzary

Answered question

2022-09-12

individual plays a game of tossing a coin where he wins Rs 2 if head turns up and nothing if tail turns up.On the basis of the given information, find (i) The expected value of the game. (4) (ii) The risk premium this person will be willing to pay to avoid the risk associated with the game.

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-29Added 106 answers

To find the expected value of the game, we need to multiply each possible outcome by its respective probability and sum them up.
Let's denote the random variable X as the amount of money the individual wins. If the coin lands on heads, the individual wins Rs 2, and if it lands on tails, the individual wins nothing. The probabilities of these outcomes are as follows:
- P(X = 2) = probability of getting heads = 1/2
- P(X = 0) = probability of getting tails = 1/2
The expected value (E[X]) of the game can be calculated as:
E[X]=(2·P(X=2))+(0·P(X=0))
Substituting the values:
E[X]=(2·12)+(0·12)
E[X]=1+0
E[X]=1
Therefore, the expected value of the game is Rs 1.
Now, let's calculate the risk premium. The risk premium represents the maximum amount of money the individual is willing to pay to avoid the risk associated with the game. It is the difference between the expected value of the game and the minimum amount the individual is willing to accept to play the game.
In this case, since the individual is not winning any money when the coin lands on tails, the minimum amount they would accept to play the game is Rs 0. Therefore, the risk premium can be calculated as:
Risk Premium = Expected Value - Minimum Amount Acceptable
Risk Premium = Rs 1 - Rs 0
Risk Premium = Rs 1
Hence, the risk premium this person will be willing to pay to avoid the risk associated with the game is Rs 1.

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