UIUC STAT 400 - Week 2 ‐ Discussion Questions

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Week 2 Discussion Questions STAT 400 D Unger Table of Contents Exercise 1 1 1 4 Exercise 1 Basic Probability 1 Exercise 2 Basic Probability 1 Exercise 3 Basic Probability 2 Exercise 4 Basic Probability 2 Exercise 5 Probability Infinite Series 2 Exercise 6 Probability Infinite Series 2 Exercise 7 Probability Infinite Series 3 A fair coin is tossed four times and the sequence of heads and tails is observed a List each of the 16 sequences in the sample space S b Let events A B C and D be given by A at least 3 heads B at most 2 heads C heads on the third toss and D 1 head and 3 tails If the probability set function assigns 1 16 to each outcome in the sample space find the following iii P B i P A iv P A C vii P B D vi P A C If P A 0 4 P B 0 5 and P A B 0 3 find c P A B a P A B ii P A B v P D b P A B Exercise 2 1 1 6 Exercise 4 Basic Probability Exercise 3 Basic Probability Exercise 5 Probability Infinite Series If P A 0 4 P B 0 5 and P A B 0 7 find the following b P A B a P A B c P A B P C 0 55 P A 0 40 P B 0 34 Suppose P B C 0 17 P A C 0 25 P A B 0 19 P A B C 0 07 Find the following c P A B C b P A B C a P A B C Find the value of p that would make this a valid probability model a Suppose S 0 2 4 6 8 i e even non negative integers and k 2 4 6 8 b Suppose S 1 2 3 4 i e positive integers and k 2 3 4 P 1 p k 2 3 4 5 6 Let a 1 Suppose S 2 3 4 5 6 and P k a Find the value of c that makes this is a valid probability distribution b Find P outcome is odd c Find P outcome is less than or equal to 5 Exercise 6 Probability Infinite Series c a k 3k P k 1 P k ln 3 P 0 p k k Exercise 7 Probability Infinite Series Suppose S 2 3 4 5 6 and P k 2 k 2 3 4 5 6 a Find the value of c that makes this is a valid probability distribution b Find P outcome is greater than or equal to 5 k c k

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# UIUC STAT 400 - Week 2 ‐ Discussion Questions

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