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HW18 - n i i X E 1 n i i X V 1 Probability distribution for...

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ECO220Y: Homework, Lecture 18 Readings: Sections 9.1, 9.3, 9.4 Exercises: 9.5, 9.6, 9.8, 9.10, 9.16, 9.22, 9.28, 9.48, 9.50, 9.54 Applets (CD-ROM): Applet 10 (page 302), Applet 11 (page 303), Applet 12 (page 303), Applet 14 (page 317) Problems: (1) It is true that: “A linear combination of independent normally distributed random variables yields another normal random variable.” Is it true that the sum of two independent uniformly distributed random variables yields another uniform variable? (2) Given the following, find the distribution of W. ) , ( ~ 2 X X N X and ) , ( ~ 2 Y Y N Y W = a + b X + c Y (3) Given the following information about two independent random variables X and Y, draw the distribution of W if W = (X – Y). Include the parameters of the distribution of W in your answer. (4) Suppose a population is uniformly distributed with a = 0 and b = 100. Suppose that X i represents the i th random draw from the population: X i ~ U[0,100]. Given this information, fill in the table below. Sample size: n

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Unformatted text preview: n i i X E 1 n i i X V 1 Probability distribution for n i i X 1 (name of the distribution) X E s.e. of ࢄ ഥ Probability distribution for ࢄ ഥ (name of the distribution) 1 2 5 30 100 .1 .2 .3-20-15-10-5 X mean:-10, s.d.:2 .1 .2 .3 5 10 15 20 Y mean:10, s.d.:2 (5) Consider rolling fifty die and creating a random variable that is the sum of the values shown. Find the continuous probability distribution that approximates this discrete probability distribution and give its parameters. (6) From Lecture 18 recall the claim of the small town in Ontario: “Average House price in the town is \$234,000 and the s.d. is \$70,000.” You have surveyed 49 houses in the town and found a sample mean of \$270,000. If what the town says is true, 95% of the time the sample mean should be in what interval? Calculate that interval and interpret it. What can we conclude from the fact that 270,000 is not in the interval?...
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• Spring '11
• tanaka
• Probability distribution, Probability theory, probability density function, Discrete probability distribution, Continuous probability distribution

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HW18 - n i i X E 1 n i i X V 1 Probability distribution for...

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