mid1s.pdf

mid1s.pdf - STAT3510:0CCC Biostatistics(Spring 2018 1...

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STAT3510:0CCC Biostatistics (Spring 2018) 1 Spring 2018, STAT3510:0CCC Biostatistics, Midterm #1 Midterm #1 Solutions 1. [10 points] For Mexican American infants born in Arizona in 1986 and 1987, the probability that a child’s gestational age is less than 37 weeks is 0.142 and the probability that his or her birth weight is less than 2500 grams is 0.051. Furthermore, the probability that these two events occur simultaneously is 0.031. Let A be the event that an infant’s gestational age is less than 37 weeks and B the event that his or her birth weight is less than 2500 grams. (a) [3 points] Are A and B independent? Why? (b) [3 points] For a randomly selected Mexican American newborn, what is the probability that A or B or both occur? (c) [4 points] What is the conditional probability that event B occurs given that event A occurs? (a) We have P ( A B ) = 0 . 031 and P ( A ) P ( B ) = 0 . 142 × 0 . 051 = 0 . 0072. So P ( A B ) 6 = P ( A ) P ( B ). Thus A and B are not independent. (b) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = 0 . 142 + 0 . 051 - 0 . 031 = 0 . 162 .

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