Question 5 ASAP PLEASE 4. (20 points) Let Y be a continuous randon variable with

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Question 5
ASAP PLEASE

4. (20 points) Let Y be a continuous randon variable with the probability density function fy (y) c(va 1) if is y s 4 and fy (y) 0 otherwise (a) Find the value of c for which (w) is a pdf. (b) Find PO 3). (c) Find P(2 s Y s 3) (d) Find P (2 Y 5. (15 points) Suppose that a game is to be played with a single fair die. In this game a player wins S20 if a 2 turns up, wins $40 if a 4 turns up, loses $30 if a 6 turns up, while the player neither wins nor loses if any other face turns up. Find the expected sum of money to be won 6. (20 points) A continuous random variable Y has the probability density function (pdf) given by fr(u) 3y2 if 0 s ys 1 and f (y) 0 otherwise. Find E(Y), E(Y 2), E(Y2), Var(Y) and ov.

Explanation / Answer

5.

As per your request answer to question 5 with explanation:

Each die side comes with a p = 1/6

If 1,3,5 comes up there is no wins , no losses, Only 0
If 2 or 4 come up, 20 or 40 are won with probability =1/6
If 6 comes up, with 1/6 probability loose $30

So, the exp. sum of money to be won = 1/6 (20+40) - 1/6(30)
= 10-5 = $5 is to be won

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