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# Assign6 - STA 3032 Assignment 6 Problem 5.40 Law of Large...

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STA 3032 – Assignment 6 Problem 5.40: Law of Large Numbers – flipping a balanced coin. What is the probability that the proportion of heads is between 0.49 and 0.51? a.) Coin flipped 1000 times. 4908 . 0 2546 . 0 7454 . 0 ) 66 . 0 ( ) 66 . 0 ( 250 500 5 . 510 250 500 5 . 489 Pr ) 510 490 Pr( = - = - - = - - = F F Z H b.) Coin flipped 10000 times. 9556 . 0 0222 . 0 9778 . 0 ) 01 . 2 ( ) 01 . 2 ( 2500 5000 5 . 5100 2500 5000 5 . 4899 Pr ) 5100 4900 Pr( = - = - - = - - = F F Z H Problem 5.46: a.) Probability of error between 0.010 and 0.015? 10 . 0 050 . 0 005 . 0 ) 015 . 0 010 . 0 Pr( = = X b.) Probability of error between –0.012 and 0.012? 48 . 0 050 . 0 024 . 0 ) 012 . 0 012 . 0 Pr( = = - X Problem 5.58: Exponential random variable with a mean of 50. a.) Probability that setting lasts for less than 20 days: 32968 . 0 1 1 ) 20 Pr( 4 . 0 50 / 20 = - = - = - - e e X b.) Probability that setting lasts at least 60 days: 30119 . 0 ) 1 ( 1 ) 60 Pr( 2 . 1 50 / 60 = = - - = - - e e X Problem 5.60:

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a.) Probability of successive calls in less than 0.5 minute? 25918 . 0 1 1 ) 5 . 0 Pr( 3 . 0 ) 6 . 0 )( 5 . 0 ( = - = - = < - - e e X b.) Probability of successive calls in more than 3 minutes? ( 29 1653 . 0 1 1 ) 3 Pr( 8 . 1 8 . 1 = = - - = - - e e X Problem 5.64: 263901 . 0 ) 125795 . 6 ( 861894 . 5 ) 1 9 . 0 ( 10 ) 1 9 . 0 ( 9 9 1 10 1 9 9 . 0 10 9 . 0 90 9 ) 1 ( 10 ) 1 ( 90 ] ) 1 ( ) 1 [( 90
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