**Unformatted text preview: **(f) If the gambler plan is to quit playing after he has had a total of ten winning days, what is the expected number of days he gambles? 3. The density function of X is f ( x ) = c x + x 3 , ≤ x ≤ 1 and is 0 otherwise. (a) Find c . (b) Find the density function of Y = X 2 . (c) Find E [ Y ]. 4. On each transaction, the amount of money withdrawn from an ATM machine is a random variable with mean 10 and variance 4, with the amounts withdrawn in diﬀerent transactions being independent. (a) What is the expected value of the total amount of money withdrawn in the next 25 transactions? (b) What is the standard deviation of the total amount of money withdrawn in the next 25 transactions? (c) Approximate the probability that the total amount of money withdrawn in the next 25 transactions exceeds 300. 1...

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- Spring '05
- Ross
- Variance, Probability theory, probability density function, gambler