set6

# First Course in Probability, A (7th Edition)

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: Sixth Homework Set — Solutions Chapter 4 Problem 55 P (no errors) = P (no errors | first typist) P (first typist) + P (no errors | second typist) P (second typist) = 1 2 parenleftbigg 3 0! e- 3 + 4 . 2 0! e- 4 . 2 parenrightbigg = 1 2 ( e- 3 + e- 4 . 2 ) . Problem 57 X is Poisson with parameter λ = 3. (a) P { X ≥ 3 } = 1- P { } - P { 1 } - P { 2 } = 1- e- 3 ( 1 + 3 + 9 2 ) = . 5768 . (b) P { X ≥ 3 | X ≥ 1 } = P { X ≥ 3 } P { X ≥ 1 } = P ( X ≥ 3) 1- e- 3 = 0 . 6070 . Problem 59 Let X be the number of times you win a prize. Then X is binomial with n = 50 and p = 1 100 , i.e., we can use the Poisson approximation with λ = 50 · 1 100 = 1 2 . (a) P { X ≥ 1 } = 1- P { X = 0 } = 1- e- 1 2 = 0 . 3935 (b) P { X = 1 } = 1 2 e- 1 2 = 0 . 3033 (c) P { X ≥ 2 } = 1- P { X = 0 } - P { X = 1 } = 1- e- 1 2 ( 1 + 1 2 ) = . 0902 Problem 61 Let X be Poisson with parameter λ = 1000 · . 0014 = 1 . 4. Then P { X ≥ 2 } = 1- P { X = 0 }- P { X = 1 } = 1- e- 1 . 4 (1+1 . 4) = 0 . 4082 .....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

set6 - Sixth Homework Set — Solutions Chapter 4 Problem...

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

View Full Document
Ask a homework question - tutors are online