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Unformatted text preview: STAT 3502 Solution for assignment # 2 Total mark=25 1. Two fair six-sided dice are tossed independently. Let M = maximum of the two tosses. a.  What is the pmf of M ? b.  Determine the cdf of M and graph it. Sol: 2.  Let x = the outcome when a fair die is rolled once. If before the die is rolled you are offered either 1 3 . 5 dollars or h ( x ) = 1 x dollars , would you accept the guaranteed amount or would you gamble? Note: It is not generally true that 1 E ( X ) = E ( 1 X ) Sol: 3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a r.v. x with pdf f ( x ) = ( 2(1- 1 x 2 ) 1 x 2 o.w. a. [1.5] Compute the cdf of x . b. [1.5] What is the value of (median)? 1 c. [1.5] Compute E ( X ) and V ( X ). d. [1.5] If 1.5 thousands gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.5 thousands gallons is expected to be left at the end of the week. (Hint: Let h ( x ) = amount left when demand = x . Sol: 4. It has been reported that approximately 60% of U.S. households have two or more television sets. Suppose that n = 15 U.S. households are sampled and x is the number...
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This note was uploaded on 09/27/2010 for the course STAT 104157 taught by Professor Jhonbran during the Spring '09 term at California Coast University.
- Spring '09