math 411 homework6

math 411 homework6 - 2 9 6.3 Consider f x = c(1-x 2...

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Texas A&M University Department of Mathematics Fall 2011 Volodymyr Nekrashevych Math 411 — Problem Set 6 Issued: 10.17 Due: 10.24 6.1. A group of 20 people go out to dinner. 10 go to an Italian restaurant, 6 to a Japanese, and 4 to a French restaurant. The fractions of people satisfied with their meals were 4/5, 2/3, and 1/2 respectively. The next day the person you a talking to was satisfied with what they ate. What is the probability that they went to the Italian restaurant? 6.2. Fill in the rest of the joint distribution so that X and Y are indepen- dent. There are two possible answers. X = 0 X = 1 Y = 0 ? 2 / 9 Y = 1
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Unformatted text preview: 2 / 9 ? 6.3. Consider f ( x ) = c (1-x 2 ) for-1 < x < 1 and 0 otherwise. What value of c should we take to make f a density function? 6.4. Suppose X has density function x-2 / 3 / 21 for 1 < x < 8 and 0 other-wise. Find EX , E ( X 2 ), and var( X ). 6.5. Suppose X has density function F ( x ) = x/ 2 for 0 < x < 2 and 0 otherwise. Find P ( X < 1) and P ( X > 3 / 2). 6.6. Suppose X has density function f ( x ) = 4 x 3 for 0 < x < 1 and 0 otherwise. Find (a) the distribution function F ( x ) = P ( X ≤ x ), (b) P ( X < 1 / 2), and (c) P (1 / 3 < X < 2 / 3)....
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