Consider a game of chance consisting of a single trial withexactly two outcomes, which from a players perspective we will call\"win\" and \"lose.\" To play the game, a player must wager an amount,which we will denote by a. If the player loses the game, aplayer loses their wager. If the player wins the game, then theykeep their wager and they win $1.00. Denote the probability byp, where 0 < p < 1. Let the random variableX denote the amount won by the player.
A) Find the sample space of the random variable X.
B) Find the pmf of the distribution of the random variableX.
C) Compute the expression for E(X), the expected valueof X.
D) A game is said to be fair if the expected amount won is 0.For what value of a, the amount wagered, would the game bedescribed as a fair game?
E) For what vaules of a is E(X) >0?
F) For what values of a is E(X) <0?
G) Suppose a person is only willing to play if their expectedamount won is non negative. For what values of a wouldthis person be willing to play, and what values of a wouldthis person not be willing to play?
