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School
University of California, Berkeley **We aren't endorsed by this school
Course
STAT W21
Subject
Statistics
Date
Aug 7, 2023
Pages
1
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SticiGui: The Multinomial distribution and the Chi-Squared Test for Goodness of Fit The Multinomial Distribution and the Chi-Squared test for Goodness of Fit Problem 1 Consider dealing a hand of 3 cards from a well shuffled standard deck of playing cards. Let X1 be the number of Aces in the hand; let X2 be the number of sevens in the hand; and let X3 be the number of cards in the hand that are neither Aces nor sevens. The random variables {X1, X2, X3} have a multinomial joint distribution. (Q1) m Problem 2 Consider drawing 4 cards at random with replacment from a standard deck of playing cards. For this problem, consider Aces to be face cards, not numbered cards. Which of the following sets of variables have a multinomial joint distribution? (select all such sets) ? the number of kings drawn, and the number of other cards drawn m the number of spades drawn, the number of hearts drawn, and the number of diamonds drawn the number of kings drawn, the number of hearts drawn, and the number of twos drawn the number of face cards drawn, the number of even-numbered cards drawn, and number of odd-numbered cards drawn (@2) the number of face cards drawn, the number of kings drawn, and the number of other cards drawn Check Answer Problem 3 A bowl contains 30 balls of various colors: color |turquoise|umberlwhitelgraylluschial ballsinbow| 5 | 8 | 6 |5| 6 | Consider drawing a random sample of size 8 with replacement from the bowl. Fill in the following table of expected values of the numbers of balls of each color in the random sample. Fill in the expected values color | turquoise | umber | white | gray | fuschia | expected number|(Q3) 1.33 @4 213 ?@s) 1.6 2 @e) 1.32 @7 159 il Consider the following possible outcome of drawing the random sample: color |(urquoise|umber|whitelgraylfuschial ballsinsamplel 0 | 3 | 3|0 2 | The probability of this outcome is (Q8) 0.0034 m The chi-squared statistic for this outcome is (Q9) 4.31 m Is the chi-square curve with 4 degrees of freedom a good approximation to the probability histogram of the chi-squared statistic for a random sample of size 8 with replacement from this bowl? (Q10) m Problem 4 The area under the chi-square curve with 22 degrees of freedom from 15.4 to 35.3 is (Q11) 0.81 m The 40% percentile of the chi-square curve with 22 degrees of freedom is (Q12) 19.76 m
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