BK plays a game, which assigns a number (Z)that is the continuous random variable with the density function
(z) =1/5,0≤z≤5
0, otherwise.
If the game assigns a number less than or equal to, then he loses 10 dollars, on the other hand, if the game assigns a number larger than, then he will gain 10 dollars. (a) Find the expected profit of the game. (b) Find the variance of the profit. (c) If you were to play this game 10 times, what is the probability that you gain 20 dollars?