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lab3 - skewed a very small amount to the left The standard...

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Alexandra Linder MATH 1710 Th 1:25 PM Lab 3 1. x=binomial random variable n=10 p=.9(same throughout lab) This histogram is not symmetrical. It is skewed to the left. 2. n=20 When n=20, the histogram is unimodal and skewed to the left. The median is 16.5. The spread is relatively small-the range is only 5. n=50
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a. When n=50, the histogram is unimodal and more symmetrical than when n=20. It is still skewed a bit to the left. b. Theoretical Mean: E(X)= 50 x .9= 45 Standard Deviation: sq rt(Var X)=sq rt(45x.1)=sq rt(4.5)=2.12 c. The actual mean acquired in the simulation was 45.011, which is a bit higher than the theoretical mean. The actual standard deviation is also higher than the theoretical, but only by .04. Both values are very close to the theoretical values. n=100 a. When n=100, the histogram is even closer to being symmetrical, and is only
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Unformatted text preview: skewed a very small amount to the left. The standard deviation is larger than when n=50. b. Theoretical mean=E(X)=100 x .9=90 Std Deviation= sq rt(Var X)=sq rt(90 x .1)=sq rt(9)=3 c. The mean is a little smaller than expected, but the standard deviation very close to the theoretical value. n=2000 a. This histogram is closer to the normal approximation. It is unimodal and there is an outlier at the lower end of the histogram. It is almost symmetrical. The standard deviation is even larger now, due to the larger sample size. b. Theoretical mean= E(X)=2000 x .9=1800 Std Deviation= sq rt(Var X)=sq rt(1800x.1)=sq rt(180)=13.42 c. The mean is only .16 higher than the theoretical value and the standard deviation is also a bit larger....
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