solutions HMWK 2

solutions HMWK 2 - ISDS-361A Solutions 2 Panayiotis Skordi...

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ISDS-361A Solutions 2. Probability, Counting, Binomial Distribution Panayiotis Skordi 1. Let x represent the number of times a student visits a bookstore in a one month period. Assume that the probability distribution of x is as follows: x 0 1 2 3 p(x) 0.05 0.25 0.50 0.20 a. Find the mean μ . b. What is the probability that the student visits the bookstore at least once in a month? c. What is the probability that the student visits the bookstore at most twice a month? Solution 1 a. = = = n i i i x P x x E 1 ) ( ) ( μ in our case n has 4 values 0, 1, 2 , 3 . So we add 85 . 1 20 . 0 * 3 50 . 0 * 2 25 . 0 * 1 05 . 0 * 0 = + + + = b. At lest once in a month tells us either 1 or 2 or 3 times in a month. So we need 95 . 0 20 . 0 50 . 0 25 . 0 ) 3 ( ) 2 ( ) 1 ( = + + = + + P P P c. At most twice means 0 or 1 or 2 So we need 80 . 0 50 . 0 25 . 0 05 . 0 ) 2 ( ) 1 ( ) 0 ( = + + = + + P P P 1
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2. In a race with 8 runners how many runners can finish first, second and third? Solution 2 The order obviously is important here. We will use the formula for permutations. )! ( ! r n n P r n - = where n is 8 and r is 3 336 120 40320 ! 5 ! 8 )! 3 8 ( ! 8 )! ( ! = = = - = - = r n n P r n ways. 3. A combination lock has a total of 30 numbers and will unlock with the proper 4 number sequence. How many possible combinations are there? Solution 3
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solutions HMWK 2 - ISDS-361A Solutions 2 Panayiotis Skordi...

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