2027Hmwk6

# 2027Hmwk6 - ISyE 2027 R D Foley Probability with...

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ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 6 October 17, 2011 due Monday 1. Suppose X has p.d.f. f ( t ) = 2 t for 0 6 t 6 1 . Compute (a) Pr { 1 / 4 6 X < 3 / 4 } , (b) E [ X ] , (c) E [ X 2 ] , (d) the variance of X , and (e) the c.d.f. of X . 2. Suppose Z has p.d.f. f ( s ) = ce - 5 s . Compute (a) c, (b) Pr { Z 6 2.5 } , (c) Pr { Z > 2.5 } , (d) the c.d.f. of Z , (e) Pr { Z > t } for all t > 0 , and (f) Pr { Z > t + s | Z > t } for all t , s > 0 . 3. Suppose Y is a random variable with mean μ and variance σ 2 < . What is the mean and variance of ( Y - μ ) . 4. Suppose a person has to pick an item from an aisle that is 50 feet in length. The person is standing at one end of the aisle. The item is a random distance L feet down the aisle from the picker. The r.v. L has p.d.f. f ( t ) = c for 0 6 t 6 50 . Determine (a) c , (b) the c.d.f. of L , (c) the mean of L , and (d) the variance of L . Assume that the person walks at 4 feet per second and takes an additional 10 seconds to pull the item out of its location. Let R be the total time for the person to walk down to location L , pull the item, and then walk back to the front of the aisle. (e) Express R as a function of L . (f) Compute the mean of R , and (g) the variance of R . 5. An earlier homework assignment contained the following: Please read the instructions carefully, before doing this problem. After reading and understanding this problem, ﬂip two coins: a nickel and a quarter. If the nickel came up heads, answer Question A. If the nickel came up tails, answer question B. Question A: Did the quarter come up heads?

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2027Hmwk6 - ISyE 2027 R D Foley Probability with...

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