2027Hmwk8

# 2027Hmwk8 - ISyE 2027 Probability with Applications Fall...

This preview shows pages 1–3. 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: ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 8 November 8, 2011 due Wednesday 1. Collie eye anomaly (CEA) is an autosomal simple recessive trait. Sup- pose there are 5 pups in the litter and both the sire and dam are carriers of collie eye anomaly. Let X be the number of affected (homozygous recessive) pups in the litter. (a) What is the p.m.f. of X ? (b) What is the mean of X ? (c) What is the variance of X ? (d) What is P { X = i , Y = j } where Y is the number of pups in the litter that are carriers of CEA? (e) What is the mean and variance of X + Y + Z where Z is the number of pups in the litter that are clear of CEA? 2. Let Z have a Gaussian distribution with mean 0 and variance 1. Com- pute and memorize P {- k 6 Z 6 k } for k = 1, 2 and 3. 3. Let X have a Gaussian distribution with mean 5 and variance 9. Using only paper and pen, compute (a) P { 2 6 X 6 8 } , (b) P {- 1 6 X 6 11 } , (c) P {- 4 6 X 6 14 } , (d) P { X > 2 } , (e) P { 2 6 X 6 14 } , (f) P {| X- 5 | > 6 } and compare this answer with the bound obtained from Chebyshev’s inequality. 4. Let X have a Gaussian distribution with mean 3 and variance 25, and let Z have a standard normal distribution. Using Tables 6.1 and 6.2 in the back of our textbook, compute (a) P { X 6 12.8 } , (b) P {| X- 3 | > 9.8 } , (c) P { Z > .87 } , (d) P { Z 6- .87 } . (e) P { X > 1 | X > 2 } , 1 5. Let X have a binomial distribution with parameters n = 15 and p = 1 / 5. Let Y have a normal distribution with same mean and variance as X . (a) Using the continuity correction, give the event involving Y that would be used to approximate each of the following events involv- ing X : { X 6 3 } , { X < 3 } , { X = 3 } , { 2 < X 6 4 } ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

2027Hmwk8 - ISyE 2027 Probability with Applications Fall...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online