Consider a game of tossing a six sided fair die. If the face that comes up is 6 , the player wins Rs. 36 and he loses Rs. k^2 , where k is the face that comes up k = 1, 2, 3, 4, 5 , then the expected winning amount in this game in Rs. is...

Step-by-step solution

Let X be the random variable representing the winning amount. The possible values of X corresponding to the outcomes 1, 2, 3, 4, 5, 6 on the die are -1^2, -2^2, -3^2, -4^2, -5^2, 36 respectively, which simplifies to -1, -4, -9, -16, -25, 36 . Since the die is fair, the probability of each outcome is 1 6 . The expected winning amount is given by E(X) = x_i P(x_i) . E(X) = 1 6 (-1) + 1 6 (-4) + 1 6 (-9) + 1 6 (-16) + 1 6 (-25) + 1 6 (36) E(X) = 1 6 (-1 - 4 - 9 - 16 - 25 + 36) E(X) = 1 6 (-55 + 36) E(X) = - 19 6 Answe