STAT330 Lecture Notes - Lecture 2: Marginal Distribution

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chocolateox167

11 Aug 2016

School

University of Waterloo

Department

Statistics

Course

STAT330

Professor

Peisong Han

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(a) the support of (x, y ) is pictured below: y. Z0 (cid:0)1 x4(cid:1) dx = k(cid:20)x . 5 by symmetry k and thus k = 0 < y < 1 x2, 1 < x < 1. Therefore or f (x, y) : (b) the marginal p. d. f. of x is. P1 y < x

Related Questions

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

Y=0 Y=1

X=0
X=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?

brownhyena716

12. Let y = f(x) be defined by the equation y + 12x2 + xe4y = 13 near x = 1, y = 0. The value of f'(1) is (a) –9, (b) –7, (c) -5, (d) -10, (e) -13.

24. Let y = f(x) be defined by the equation ya +36x + 72 In(y) = 37 near x = 1, y = 1. The value of f'(1) is (a) -9, (b) -7, (c) -11, (d) -4, (e) –10.

STAT330 Lecture Notes - Lecture 2: Marginal Distribution

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Introductory Statistics

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