4604_ProblemSet1

# 4604_ProblemSet1 - PHY4604 Problem Set 1 PHY 4604 Problem...

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PHY4604 Problem Set 1 Department of Physics Page 1 of 3 PHY 4604 Problem Set #1 Due Wednesday September 6, 2006 (in class) (Total Points = 60, Late homework = 50%) Reading: Griffiths Chapter 1. Useful Math: ) ( 2 1 2 1 1 0 2 2 + + Γ = n n x a n a dx e x , where Γ (x) is the gamma function and Γ (x+1) = x Γ (x) . Γ (1) = Γ (2) = 1, Γ (n) = (n-1)! if n is a positive integer, and π = Γ ) ( 2 1 . Integration by parts: b a b a b a fg gdx dx df dx dx dg f + = Problem 1 (12 points): Consider a room containing 14 people, whose ages are as follows: One person aged 14, One person aged 15, Three people aged 16, Two people aged 22, Two people aged 24, Five people aged 25. (a) (1 point) If you selected one person from the room, what is the probability that the person’s age would be 15? (b) (1 point) What is the most probable age? (c) (1 point) What is the median age? (d) (1 point) What is the average age? (e) (1 point) Let N(j) be the number of people with age j. Histogram N(j) versus j. (f) (2 points) Compute <j 2 > and <j> 2 . (g) (3 points)

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4604_ProblemSet1 - PHY4604 Problem Set 1 PHY 4604 Problem...

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