tut7ans - are independent. ,0<x 1 <1; zero elsewhere...

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

View Full Document Right Arrow Icon
COMP211 Data and System Modeling (PROB/STAT) Tutorial (Week 7) Answer 1) For continuous random variables X and Y with the joint probability density function, a) Find ,,, b) Find the covariance of X, Y cov(X,Y) and the correlation coefficient of X and Y. Answer: a) =11/144 =11/144 b) =-1/144 =-1/11 2) Let random variables X1 and X2 have the joint pdf, a) Find marginal pdfs of X 1 and X 2 b) Find the conditional pdf of X 2 given X 1 = x 1 c) Find the conditional pdf of X 1 given X 2 = x 2 d) Find the conditional expectation and variance of X 2 given X 1 = x 1 e) Find the conditional expectation and variance of X 1 given X 2 = x 2 f) Find P(0< X 1 <1/2) and P(0< X 1 <1/2| X 2 =3/4) Answer: a) , 0<x 1 <1; zero elsewhere , 0<x 2 <1; zero elsewhere b) ,x 1 < x 2 <1; zero elsewhere c) ,0<x 1 < x 2 ; zero elsewhere d) ,0<x 1 <1 ,0<x 1 <1 e) ,0<x 2 <1 ,0<x 2 <1 f)
Background image of page 1

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

View Full DocumentRight Arrow Icon
3) Show that the random variables X1 and X2 with joint pdf,
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: are independent. ,0<x 1 <1; zero elsewhere ,0<x 2 <1; zero elsewhere Since , so the random variables X1 and X2 are independent. 4) One cookie in 5 is broken. If 20 are grabbed, what are (a) P(4 broken), (b) P(at most 2 broken), and (c) P(at least 4 broken)? Answer: The situation is analogous to a succession of Bernoulli trails, with a broken cookie corresponding to a success. Let X be the number of broken cookies. Hence p=1/5, q=1-p=4/5, and n=20. Consequently, a) P(4 broken) = P(X=4) = = 0.2182 b) P(at most 2 broken) = P(X= 0 or 1 or 2) = = 0.2061 c) P(at least 4 broken) = 1 – P(X<4) = 1 – ( P(X=0) +P(X=1) +P(X=2) +P(X=3) ) = = 0.5886...
View Full Document

This note was uploaded on 04/08/2012 for the course COMP 211 taught by Professor Dr.kwok during the Spring '12 term at Hong Kong Polytechnic University.

Page1 / 2

tut7ans - are independent. ,0<x 1 <1; zero elsewhere...

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