# Suppose that the random variables Y1 and Y2 have joint probability density function, f

## Problem 5.32 Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Problem 5.32

Suppose that the random variables Y1 and Y2 have joint probability density function, f (y1, y2), given by (see Exercise 5.14) f (y1, y2) = 6y2 1 y2, 0 y1 y2, y1 + y2 2, 0, elsewhere. a Show that the marginal density of Y1 is a beta density with = 3 and = 2. b Derive the marginal density of Y2. c Derive the conditional density of Y2 given Y1 = y1. d Find P(Y2 < 1.1|Y1 = .60).

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Groups Randomize control group Split individuals into two groups separately Control vs. treatment Compare the two averages correlation between the groups (Measure the strength before and after to get the experiment) Matching Observed and match into pairs with two treatments (Longitudinal and measures) Each group has their own control group within Find the change between...

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