HW_5 - Solutions for Homework#5 7 a 0.030 b 0.025 0.015...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions for Homework #5 7. a. 0.030 b. 0.025+0.015+0.050+0.030=0.12 c. P(exactly one car)=0.05+0.03+0.02=0.07 P(exactly one bus)=0.015+…+0.03=0.3 d. P(Y=1,X=3,4,5)+P(Y=2)=(0.09+0.06+0.03)+(0.01+0.02+0.05+0.06+0.04+0.02)=0.38 e. yes, since ( , ) ( ) ( ) X Y p x y p x p y = ⋅ for all x and y. 12. a. ( 1 ) ( ) [ ] , x y x xy X xy x x f x xe dy xe e dy e xe e x x ∞ ∞- +---- ∞- = = = = <- ∫ ∫ 3 3 3 ( 3) [ ] x x P X e dx e e ∞-- ∞- = =- = ∫ b. ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) 2 2 ( ) [ ] 1 [ ( ) ] (i nt egr al by par t s) 1 1 1 [ ] , (1 ) (1 ) x y x y Y x y x y x y e f y xe dx x dx y e e x dx y y e y y y- + ∞ ∞- +- +- + ∞ ∞- + ∞- ′ = = +-- =- + + = + - = < + + ∫ ∫ ∫ Since ( , ) ( ) ( ) X Y f x y f x f y ≠ , they are not independent. c. P(at least one >3)=1-P(X<3 and Y<3) P(X<3,Y<3)=-- +--------- =- = =- =- =- + =--- ∫ ∫ ∫ ∫ ∫ 3 3 3 ( 1 ) 3 3 3 3 4 12 4 3 3 [ ] 1 ( ) ( ) 1 [ / 4] 1 ( ) 4 4 xy x y x x x x x x x e xe dydx xe dx x e xe dx e e dx x...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

HW_5 - Solutions for Homework#5 7 a 0.030 b 0.025 0.015...

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

View Full Document
Ask a homework question - tutors are online