problemset21

# Problemset21 - = √ 3 x 2 6 for-2 ≤ x ≤ 1 and f X x = 0 otherwise Find the probability that X is positive 5 6 Design your own problem and

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STAT/MA 416 October 17, 2011 Problem Set 21 Name: 1. Consider a random variable X with density f X ( x ) = ( 1 5 e - x/ 5 for x > 0, 0 otherwise. a. Find P (3 X 5). b. Find an expression for the CDF F X ( x ) of X . c. Graph the CDF F X ( x ) of X . 1

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2. Let X have density f X ( x ) = kx 2 (1 - x ) 2 for 0 x 1, and f X ( x ) = 0 otherwise, where k is constant. a. Find the value of k . b. Find P ( X 3 / 4). 2
3. Assume X has constant density on the interval [0 , 25], and the density of X is 0 otherwise. Find P (13 . 2 X 19 . 9). 3

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4. Suppose X has CDF F X ( x ) = 0 if x < 0, x 4 (5 - 4 x ) if 0 x 1, 1 if x > 1. a. Find P ( X > 1 / 2). b. Find the density f X ( x ) of X . 4
5. Let X have density f X ( x

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Unformatted text preview: ) = √ 3( x +2) 6 for-2 ≤ x ≤ 1, and f X ( x ) = 0 otherwise. Find the probability that X is positive. 5 6. Design your own problem and solution. Create your own problem about a contin-uous random variable. Design your problem in such a way that you would ﬁnd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
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## This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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Problemset21 - = √ 3 x 2 6 for-2 ≤ x ≤ 1 and f X x = 0 otherwise Find the probability that X is positive 5 6 Design your own problem and

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