SP4C_EC41_key - EC 41 UCLA Sample Problems#4C Sections 4.3...

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Unformatted text preview: EC 41; UCLA; Sample Problems #4C Sections 4.3, 5.1, 5.2 I) Consider an experiment: flip a coin three times and count the number of heads. Suppose this experiment is repeated four times with the following results: 2 _ 4.. I _ 2. _ 7 2 fl, 7- J_ 3 ~17. 3"- i) HHH; ii) HTT; iii) Tl-IH; and iv) TH? S ‘— '*IJ:C Ll 4- 6 ZJ K J [ j 5 l 2 : 7E— a)Whatisthesamlemeanof)[email protected] \ - p D ‘2’} ' m b) What is as sample standard deviation of X? t’) 0) Draw a histogram showing your actual outcomes below to the left, with X values on the horizontal axis and relative frequency of X on the vertical axis. d) Draw the true probability histogram (probability density function), below to the right, with X values on the horizontal axis and the true probability of the corresponding X value on the vertical axis. histogram for 4 observations true probability histogram rein whpowmv P”) hwy 2) a) Go to the Simple Random Sample applet on the publishers web site. Note what ha- nens to number entries in the population hopper as sample size increases. Does this represent sampling with or b) choose a sample of 10 How many of the number m the sample are even? [ 3% L{ M #964! I? 1”] 9 6 auswt tfi very c) If your repeatedly took samples of 10 what would be the average number of even numbers in a large number of males? (2 ppm-w c: %) 'ra) Go to the publisher’s“ °- 2:: mm - ” Roll 4 dice. What is the population mean of sum of spots? - b ) What happens to the average of the Sum of spots as the four die are rolled more and more? ’3. Q 5 5“} 3. 5’ IL/ (A {t We elm in M7 pant-Wm mam Ll) Go to the Textbook’s website ~ Statistical Applets — Probability. What happens to the sample proportion of tails as more and more tosses are undertaken? GPPWUUMS ‘ll‘W. @101leth Hi ply/Sterile; : IS— 5) Assume the probability of birthdays falling on any one ofthe days ofa standard year is the same (ignore leap years)! In a class of2 tudents wh t is thep bab that two or more of the students hav u ‘ ._ e birthday? [a as: a; {,3 ”p21“ c L ._ Wrigk KT? at s~ ‘ l P . / 3 I 3 ‘ _ 6) 3) Suppose the probability of Bob getting an “'A in 3in class is .3 (30%). Assume he takes three classes per term and his grades in class are independent of one another. Let X be a random variable for the number ofA’s Bob earns in one term. Write the 4 possible X values and the probability associated'with each: X P1X] (may use binomial! . o 314 3 t [3) (:7) t fiat : 3 C 3) C 7)? Z , I 57 x 3 (3) C 7) 3 . a 2 —; = l (3330 )0 .—...—-—-—"—F"'" t b) Suppose Bob’é grades for 4 terms are B B B' A 13 c; A c C' and A A D. What are the sample mean and sample standard deviatiOn of X for these 4 terms, 1?: [email protected] 5x: a Q l [email protected] LCIQHCJQ éqffif Ma oil: g ,6665 What are the true mean and standard deviation of X?p, {1M =- it): .MBCW muOH man 1027(3) = m : .7‘7‘3726“ 77¢ :.—3tia(o 9) it 441C911 Craig—.1?) + ”761(1) 27% we” 2297+ M, —,63 0) Draw a histogram showing your actual outcomes below to the left, with X values on the horizontal axis and relative frequency of X on the vertical axis. d) Draw the true probability histogram (probability density function), below to the right, with X values on the horizontal axis and the true probability of the corresponding X value on the vertical axis. h' togram for 4 observations true probability histogram ”Willi? lJWDWL‘lt'l-f l lulDICi‘le 5114” _, 3‘13 t2? .027 ...
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