set3solutions - IE 300 / GE 331 Discussion Problem Set 3...

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: IE 300 / GE 331 Discussion Problem Set 3 • 3-76 Let X denote the number of patients with heart failures due to outside factors. Then it has a binomial distribution with n= 20 and p= 0.13. Note that the pmf for a binomial random variable is as follows: P(X=k) = ? ¡ ¢£ ¡ (1 − £ ) ?−¡ (a) P(X=3)= 20 3 ¢£ 3 (1 − £ ) 17 = 0.235 (b) P(X≥3)= 1-P(X<3) = 1-P(X=0)-P(X=1)-P(X=2) = 0.492 (c) µ= E(X)= np= (20)(0.13)= 2.6 Var(X)= E[(X- µ) 2 ]= np(1-p)= 2.262 σ= ¤ Var(X) = 1.504 • 3-78 (a) X is a binomial random variable with n = 20 and p = 0.01, so E(X) = np= 20 (0.01) = 0.2 Var(X) = np(1-p)= 20 (0.01) (0.99) = 0.198 E(X)+3 ¤ Var(X) = 0.2 + 3 √ 0.198 =1.53 P(X>1.53) = P(X≥2) = 1-P(X<2) = 1- ¥ 20 ¢ (0.01 )(0.99 20 ) + 20 1 ¢ (0.01 1 )(0.99 19 ) ¦ = 0.0169 (b) X is a binomial random variable with n = 20 and p = 0.04, so P(X>1) = 1- P(X≤1) = 1- ¥ 20 ¢ (0.04 )(0.96 20 ) + 20 1 ¢ (0.04 1 )(0.96 19 ) ¦ = 0.189 (c) Let Y denote the number of times that X exceeds 1 in the next five samples. Note that Y is a Let Y denote the number of times that X exceeds 1 in the next five samples....
View Full Document

This note was uploaded on 03/16/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

Page1 / 2

set3solutions - IE 300 / GE 331 Discussion Problem Set 3...

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