Reference no: EM132858331

Alex is playing a gambling game with a friend. Each round, he needs to bet $2. If he wins, he can get the bet back and then gain $5; otherwise, he loses the bet. He can win each round of game with a probability of p = 0.6. Suppose each round of game is independent from each other.

a) Find the probability distribution of the number of rounds Alex wins after 5 rounds of game.

b) Find the expected number of rounds Alex wins after 5 rounds of game and the corre sponding variance by defifinition.

c) Find the expected amount of Alex's net gain after 5 rounds of game and the corre sponding variance by defifinition.

Question

The random variable X has the following density function:

f(x) = (x-6)/c 6 ≤ x ≤ 12 0 elsewhere where c is a constant.

a) Find the constant c.

b) Find E(X) and Var(X)

c) Find the median of X.