individual plays a game of tossing a coin

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2022-03-30

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

star233

star233

Skilled2023-04-26Added 403 answers

We are given that an individual plays a game of tossing a coin, where they win Rs 2 if a head turns up and nothing if a tail turns up. We need to find (i) the expected value of the game and (ii) the risk premium this person will be willing to pay to avoid the risk associated with the game.
(i) The expected value of the game is given by the formula:
E(X)=ixiP(X=xi)
where X is the random variable representing the winnings of the game, xi are the possible values of X, and P(X=xi) is the probability of X taking the value xi. In this case, we have two possible outcomes: a head with probability p=0.5 and a tail with probability q=1p=0.5. The corresponding winnings are X=2 for a head and X=0 for a tail. Thus, the expected value of the game is:
E(X)=(2)(0.5)+(0)(0.5)=1
Therefore, the expected value of the game is Rs 1.
(ii) The risk premium is the amount of money that the person is willing to pay to avoid the risk associated with the game. It is equal to the difference between the expected value of the game and the minimum amount that the person is willing to accept as a guaranteed payoff. In this case, if the person is risk-neutral, they would be willing to accept the expected value of the game as a guaranteed payoff, which is Rs 1. If the person is risk-averse, they would demand a risk premium to compensate for the risk of losing. The amount of risk premium that the person would be willing to pay depends on their degree of risk aversion. For example, if the person is very risk-averse, they may demand a risk premium of Rs 0.50 or more.

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