homework_1_sol

# homework_1_sol - 2028 Basic Statistical Methods Solutions...

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Unformatted text preview: 2028: Basic Statistical Methods Solutions - Homework 1 II Random Variables 1 Let X be the time between two successive arrivals at the drive-up window of a local bank. i. Since the events occur according to a Pois ( λ = 10) distribution, then X , the time between successive events per hour, is exp ( λ = 10) . ii. If X ∼ exp ( λ ) then X is memoryless. In other words, P ( X > a + b | X > a ) = P ( X > b ) . We need to find P ( X > . 5 | X > . 25) . According to the observation above: P ( X > . 5 | X > . 25) = P ( X > . 25) = 1- P ( X ≤ . 25) = 1- (1- e- 10 × . 25 ) = e- 2 . 5 ≈ . 0881 2 Let X be the number of neurons that have higher firing rates for Condition 1. Then we assume X ∼ B (100 , . 58) . (a) We want P ( X = 90) . This is the value of the binomial pdf at x = 90 . The R command used is dbinom(90,100,.58) We get P ( X = 90) ≈ (b) We want P (40 ≤ X ≤ 60) = P ( X ≤ 60)- P ( X < 40) = P ( X ≤ 60)- P ( X ≤ 39) ....
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homework_1_sol - 2028 Basic Statistical Methods Solutions...

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