Quiz2-Answer - Probability: Quiz II May 25, 2004 1. A...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Probability: Quiz II May 25, 2004 1. A filling station is supplied with gasoline once a week. Suppose its weekly volume of sales in thousands of gallons is a random variable with probability density function f ( x ) = ‰ 5(1- x ) 4 < x < 1 otherwise How large must the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is 0.01? (5%) Sol) We want to find c such that P ( X > c ) = 1- F ( c ) = 0 . 01. For 0 < x < 1, we have F ( x ) = Z x 5(1- t ) 4 dt = 1- (1- x ) 5 Solving the following equation: 1- F ( c ) = 1- [1- (1- c ) 5 ] = 0 . 01 , we get c = 1- . 01 1 / 5 ≈ . 601. Hence, the tank capacity is required to be 601 gallons. 2. The joint probability density function of X and Y is given by f ( x,y ) = e- ( x + y ) , ≤ x < ∞ , ≤ y < ∞ . (a) Find P ( X ≤ Y ). (5%) Sol) P ( X ≤ Y ) = Z ∞ Z ∞ x e- ( x + y ) dydx = Z ∞ e- x Z ∞ x e- y dydx = Z ∞ e- 2 x dx = 1 2 (b) Find P ( X ≤ a ). (5%) Sol) f X ( x ) = Z ∞ e- ( x + y ) dy = e- x , x > P ( X ≤ a ) = Z a e- x dx = 1- e- a , a > 3. Let T be the region bounded by the lines y = 0, y = x , and x = 1, as was shown in the following figure. y = 0 x =1 y = x x y y = 0 x =1 y = x x y Suppose that f is a function defined by f ( x,y ) = cxy for ( x,y ) in T , and that f ( x,y ) = 0 when ( x,y ) is not in T ....
View Full Document

This note was uploaded on 12/22/2011 for the course CS 101 taught by Professor Dat during the Spring '11 term at Bilkent University.

Page1 / 4

Quiz2-Answer - Probability: Quiz II May 25, 2004 1. A...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online