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ps01 - Statistics 403 Problem Set 1 Due in lab on Friday...

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Statistics 403 Problem Set 1 Due in lab on Friday, September 17th 1. Suppose we have the following probability distribution: x P ( X = x ) 1 0.19 2 0.09 3 0.07 4 0.15 5 0.21 6 0.03 7 0.01 8 0.03 9 0.12 10 0.10 (a) What is the probability that X is odd? Solution: The probability that X is odd is 0 . 19 + 0 . 07 + 0 . 21 + 0 . 01 + 0 . 12 = 0 . 6 . (b) What is the probability that X is evenly divisible by 3? Solution: X is evenly divisible by 3 only if X equals 3, 6, or 9. Thus the probability is 0 . 07 + 0 . 03 + 0 . 12 = 0 . 22 . (c) Are these two events independent? Why or why not? Solution: If the events are independent, the probabilities must satisfy the mul- tiplication rule. The value of X is both odd and evenly divisible by 3 only if X equals 3 or 9. This probability is 0 . 07+0 . 12 = 0 . 19, which is substantially greater than the product 0 . 6 × 0 . 22 (where 0 . 22 is the probability that X is divisible by 3). Thus these two events are not independent (they are positively dependent). (d) Construct the cumulative probability distribution for this random variable.
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