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samplemidterm1

# samplemidterm1 - AMS 310 MIDTERM I NAME Total score 120...

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AMS 310 10/22/2007 MIDTERM I NAME _______________________ ID ________________________ Total score: 120 points Show all your work for full credit 1. (15 points) Given a set of observations 3.5 1.4 6.6 6.0 4.2 4.4 5.3 5.6 6.8 2.5 5.4 (a) Find the 90 th percentile. (b) Find the minimum, maximum, range, and interquartile range. (c) Draw a boxplot. 2. (12 points) X is a discrete random variable with probability distribution P(X= -1)=0.1, P(X=0)=0.2, P(X=1)=0.2, P(X=3)=0.3, P(X=5)=0.2 (a) Find P(X<0.5), P(X<1), P(X<4.2), and P(X<6) (b) Compute the mean and variance of X.

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3. (12 points) A shipment contains 6 defective items and 14 non-defective items. 5 items are selected at random without replacement. Let X be the number of defective items obtained, (a) find the distribution of X (no just the name of the distribution!); (b) what is the probability that at least 3 defective items will be obtained? 4. (12 points) A fair coin is thrown repeatedly. What is the probability that on the n th throw: (a) a head appears for the first time? (b) the number of heads and tails to date are equal?
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