# Mid1Examples-answers - 6)-P ( X ≤ 1). We can use the cdf...

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Question 2 (10 total points) Let X be a discrete random variable with cumulative distribution function (cdf) F X ( x ) = 0 x < 1 0 . 30 1 x < 3 0 . 40 3 x < 4 0 . 45 4 x < 6 0 . 60 6 x < 12 1 12 x . (a) (4 pts) Determine the probability mass function (pmf) of the random variable X . Answer: The pmf is k 1 3 4 6 12 p X ( k ) 0.3 0.1 0.05 0.15 0.4 and p X ( x ) = 0 for all x / ∈ { 1 , 3 , 4 , 6 , 12 } . (b) (3 pts) Use the cdf to compute P (3 X 6). Be sure to show how you used the cdf to make the calculation. Answer: We need to compute P (3 X 6) which can be written as P ( X 6) - P ( X < 3). The smallest possible value less than 3 is 1, and so this is the same as P ( X

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Unformatted text preview: 6)-P ( X ≤ 1). We can use the cdf to compute this as F (6)-F (1) = 0 . 6-. 3 = 0 . 3 . (c) (3 pts) Use the pmf to compute the same probability, P (3 ≤ X ≤ 6). Be sure to show how you used the pmf to make the calculation. Answer: We can write P (3 ≤ X ≤ 6) = P ( X = 3) + P ( X = 4) + P ( X = 6), as these are the only possible values between 3 and 6 inclusive. We can use the pmf to compute this as P (3 ≤ X ≤ 6) = p X (3) + p X (4) + p X (6) = 0 . 1 + 0 . 05 + 0 . 15 = 0 . 3 . 3...
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## This note was uploaded on 04/07/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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Mid1Examples-answers - 6)-P ( X ≤ 1). We can use the cdf...

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