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Unformatted text preview: Statistics 116 - Fall 2004 Theory of Probability Midterm # 2, Practice # 1 show (and briefly explain) all of your work. calculators are permitted for numerical calculations only. Instructions: Answer 4 out of 5 questions. Clearly mark which 4 questions you decide to answer. If you do not clearly indicate which 4 are to be counted, your mark will be based on 5 instead of 4 questions, there are no bonus points. All questions have equal weight. Q. 1) Let X be a Binomial random variable with parameters n and p . Show that E 1 X + 1 = 1- (1- p ) n +1 ( n + 1) p . Solution: E 1 X + 1 = n X j =0 1 j + 1 n j p j (1- p ) n- j = n X j =0 n ! ( n- j )!( j + 1)! p j (1- p ) n- j = 1 ( n + 1) p n X j =0 ( n + 1)! ( n- j )!( j + 1)! p j +1 (1- p ) n- j = 1 ( n + 1) p n +1 X j =1 ( n + 1)! ( n + 1- j )!( j )! p j (1- p ) n +1- j = 1 ( n + 1) p ( 1- (1- p ) n +1 ) 1 Q. 2) A filling station is supplied with gasoline once a week. Suppose its weekly volume of sales in thousands of gallons is a random variable with proba-...
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This note was uploaded on 02/13/2012 for the course ECON 101 taught by Professor Teerana during the Spring '11 term at Thammasat University.
- Spring '11