1 2 3 4 5 Bonus Total Question 1 Let fxx2 for x Î 02 a Does fx satisfy the

# 1 2 3 4 5 bonus total question 1 let fxx2 for x î 02

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1 2 3 4 5 Bonus Total

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Question 1 Let f(x)=x/2 for x Î (0,2). a) Does f(x) satisfy the necessary conditions to be a density function? Explain your answer. (5 points) b) What is the cumulative distribution function associated to f(x)? (5 points) c) What is the probability that X is between 0 and 1? (5 points)

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Question 3 a) You receive three playing cards (from a pack of 52). What is the probability that you receive two cards of the same rank? Remember that there are 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king) and four suits (clubs, spades, hearts and tiles) in a card game. (7 points) b) Let A i (i=1,…,n) be n mutually exclusive and collectively exhaustive events and B j another event. Show that (8 points)
c)

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