RelativeResourceManager - um- onday, Feb. 07 in the lecture...

Info iconThis preview shows pages 1–6. 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

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: um- onday, Feb. 07 in the lecture filerSotuhons misfit—m 3 IMPORTANT NOTES: 1. You MUST write your ’I\1torial Section (it is either A1 or A2 or A3 or A4). 2. Work independently (do not work in groups with other student(s)). 3. You MUST show your work for each question. Due: 4. Assignments will n_ot be accepted after the due time and date (in fact the solutions will be posted soon after the due time and date). 5. Answer each question in the space provided (use extra pages if needed) AND staple all your pages together before submitting the assignment. Questions 1. marks] An urn contains :3 red and 3 blue chips. Suppose that 4 of these chips are selected at random and transferred to a second urn. which was originally empty. If a randomly selected chip from this second urn is blue. what is the probability that :2 red and 2 blue chips were transferred from the first urn to the second urn? Lac 8 7- ‘l'lrte. randomla §€\€C\’€6l Cw? Aerom Urh‘#2 i? E‘EE A 2. LI. recl dud O blM JAWS we’ve *mmsfievmd L§ A3 =3 ’/ // ’/ // 1/ I, A; = Z ’/ ’/ Z " ”' ” ’/ Al :2 l J I, 3 ’7 '1 0 // P (RABX —,- PCBW‘Q PUS‘P'» , wluuu; STAT 3502 A Assignment#1 Questions 2. [5 ma.rks.f Let k 2 3 be any given integer. What is the probability that a random k-digit number will have at least one 0. at least one 1. and at least one ‘2? (Note: as usual. every number starts with either a 1. or a 2. or a 9 (but not a 0).) . ,- si— Since W \ we “0“”? Lfilhowtl K-°‘*'a*“”m‘0€m Mow/ A r. We selec‘lecl number has all 002 O aka-ML Carma-i’loe a Zero] AMWV = PCAAB (\c\ r; \— P010 B’UC’) Bil, PtA’UB'UC’ )s PtA’)+ Pte’l + P (c’) -Pux’ne’>-P(A’<\C’)-WM) + P (A’n B’nc’l c: . 4 K a“ one?“ mm“ 3 <3 3"" -‘ + \4-1 + fl- - ' pm (0|)(IOK') (MOO 5 Law”) \ L‘IlQo ) <5“ (7)66“ + 7“ .. ~———MO¥-\ " (q)(\0t<-\) (q)C\OK-\\ . STAT 3502 A Assignment#1 Questions 3. ['3 marks./' The cumulative distribution function (cdf) of a random variable X is given by: F(I):0if1<731 F(I):3/8if—3SI<0: F(I): 1/2ifOSI<3: F(I)=3/4if3§I<-1. and 17(1) : 1 if .r 2 4. Compute VLX') and E(X (Hint: First find the probability mass function of X.) STAT 3502 A Questions 4. ['3 marks}; Suppose that n integers are randomly selected from {1. 2. - - Let X be the largest number selected. Find E(.\')r Assigmnent#1 - ‘ N} with replacement. STAT 3502 A Assignment# 1 Questions 5. Short questions: 5(a). [3 marks._/ Suppose that independent Bernoulli trials with parameter p are performed successively. Let N be the number of trials needed to get .r successes, and X be the number of successes in the first n trials. Show that P(N 2 n) = f P(X : 1). mm A P W) WW3 9c r‘b-fl U! STAT 3502 A Assignment#1 5(b). [3 marksf Let the random variable X have a Poisson distribution with parameter A. Show that for every n 21 one has ELY") : AE((X ~1)"‘1). Note that. using this formula. we can find E(X).E(X2).--- recursively. ...
View Full Document

This note was uploaded on 02/15/2011 for the course SYSC 3600 taught by Professor Adsd during the Spring '10 term at Universidad Alfonso X El Sabio.

Page1 / 6

RelativeResourceManager - um- onday, Feb. 07 in the lecture...

This preview shows document pages 1 - 6. Sign up to view the full document.

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