fall01_mid1

fall01_mid1 - EEEBSO: Midterm Exam 1 Fall 2001 Examination...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EEEBSO: Midterm Exam 1 Fall 2001 Examination Date: Oct. 3rd Examination Time: 9140710130 am Student Name: __§'le0—n Student ID: 1. This exam consists of three problems. 2. One—page crib sheet is allowed. 1. Determine Whether the following statements are TRUE or FALSE (you don’t have to provide any justification for your answer. For each correct answer you will receive 5 points, for each incorrect answer 2 points will be deducted, and no points will be given for no answering. (a) Suppose 31 and B2 are two mutually exclusive events, and A is an arbitrary event. Then, onmawm=Pman+flAma1 TRuE (b) Let A and B be two arbitrary events. Then, PM fl B] 2 PM] + P[B] — 1. TR‘AE (c) Let FX denote the cumulative distribution function of a discrete random vari- able X. Then, for any x, FALSE (d) Suppose X and Y are two uncorrelated random variables. Then, var[X + Y] : var[X] + var[l/]. Time 2. (30’) The probability mass function (PMF) of a random variable X is given as follows: 1/8 3:: —2, 1/4 x: -—1, PX($)= 1/4 x=0, 1/4, a: = 1, 1/8, 33:2. Define a new random variable Y = X 2. (a) (8’) Find the probability mass function (PMF) of Y. “up, I, 4} .. yL}. 3=° PYtj’ - 3: )3, l Kr a==4 (b) (12’) Find the expectation ply and the standard deviation O'y of Y. #3: El:le 4-59.1- é-H—i-‘r: 91— . —- .‘L EEY13=¢°+J£W+¢ 16’ 3 1.. 1—1 ‘4- 4. 7"":: (71': El: Tu ‘ FY (TY : s/‘z. (C) (10’) what is the PM); _ 0'}! g Y 3 ,u + 0y]? x WW“, 0? = 3/2. “fix” °"Y 5 Y5 fix “7T1 3?[0-3/2_ éTf: Cd's/2K3 7:” “3/st5 .. _ ._ 3 _ YL3¢°J+PE343 “way? 3. (50’) The joint probability mass function (PMF) of random variables N and K is k 0 otherwise 71. —1(] 107: k=031)-I-310;n:0117"' PN‘KU’IJC) = ‘ (a) (15’) Find the marginal PMFS of N and K. o n "to ‘ {0 3 ..—-"_F' Z A} R30 ‘ _ n .. : 10 9 {w n! “(Ln)”: ( \0 (b) (10’) Find the conditional PMF of K given N. F‘Y h'L-JJ " Inn) ‘0: fl :0! ‘I - 4 thC'I'er UH“) : hm! hm) PI n|D o to :- ID :1 ( ‘RJK%) ____-_—_______ __ Q‘ ‘0" 2“" — n1 —. ‘0 L \D o - t? \,K\N(h\n‘) ': {v ( BJKZ‘ It?!" I o ’.ul. (C) (15’) Find the expectations ofN and K_ DO (5 iune_l, ELM]: E n. mm; = “Eu (a m :- =¢ (d) (10’) Are N and K correlated? Show details to justify your answer. for out; chm) 9% Ce. PENCIL») =— FAUI’NU‘) 7-? k 0.; N «we Meier-sde 5? \< V M «x: uncorrd~*¢d. ‘O ...
View Full Document

Page1 / 5

fall01_mid1 - EEEBSO: Midterm Exam 1 Fall 2001 Examination...

This preview shows document pages 1 - 5. Sign up to view the full document.

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