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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) TlIH; and iv) TH? S ‘— '*IJ:C Ll 4 6 ZJ K J [ j 5 l 2 : 7E—
a)Whatisthesamlemeanof)[email protected] \ 
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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 ppmw 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 pantWm 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?
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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!
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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
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 Spring '07
 Guggenberger

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