{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

final_old - NTHU MATH 2810 Final Examination Jan 8 2008...

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

View Full Document Right Arrow Icon
NTHU MATH 2810 Final Examination Jan 8, 2008 Note. There are 8 problems in total. The total score is 100pts. To ensure consideration for partial scores, write down intermediate steps where necessary. 1. ( 16pts, 2pts for each ) For the following statements, please answer true or false. If false, please explain why. (a) Let X be a continuous random variable, then P ( X A ) = 0 for any countable set A . (b) For a continuous random variable, the values of its probability density function (pdf) must be between 0 and 1. (c) Transformation by using Jacobian can be applied to find the joint pdf when the mapping between two groups of n random variables is not one-to-one. (d) A random variable X with possible values 0 and 1 will have E ( X k ) = E ( X ) for k = 2 , 3 , 4 ,... . (e) Let X 1 ,...,X n be i.i.d. from a distribution with finite variance. The variance of X n = ( X 1 + ··· + X n ) /n always tends to zero as the sample size n increases to infinity. (f) The correlation coefficient of two independent random variables is zero. (g) If X and Y are uncorrelated, then E ( X | Y ) = E ( X ). (h) If X and Y are independent, then E ( XY ) = E ( X ) E ( Y ) and E ( X/Y ) = E ( X ) /E ( Y ). 2. ( 15pts, 3pts for each ) For each of the random variables X below, determine the type of distribution (i.e., Normal, Exponential, Gamma, Beta, Uniform, Poisson, Hypergeomet-
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

final_old - NTHU MATH 2810 Final Examination Jan 8 2008...

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

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online