Suppose x has a multivariate normal distribution given by X1 1 2р 0 Х— X2 N3 2р 4 X3 3 9. When p = 0.5 , answer the following questions. 3X1 – X2 follows a/an (). distribution with mean and variance equal to _(b)_ v Choose... respectively. Fill in the blanks. (a) normal, (b) 1 and 5 (a) gamma, (b) 1 and 4 X, and X, are independent. Answer this question with True or False. 1/4 1/2 (a) gamma, (b) 1/2 and 6 (X1 – X2 + 1)² follows a/an _(a)_ distribution with parameters _(b). Fill in the (a) normal, (b) 1 and 7 blanks. (a) gamma, (b) 1 and 7 (a) normal, (b) 2 and 7 (a) gamma, (b) 1/2 and 4 What is the conditional variance of X, given (X2, X3) = (1, 1) ? True 1 3/4 (a) gamma, (b) 1/2 and 8 (a) normal, (b) 2 and 5 ba

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Suppose X has a multivariate normal distribution given by
X1
1
1 2р 0
X =
X2
· N3
2p 4 0
X3
3
0 0 9
When p = 0.5 ,answer the following questions.
3X1 – X2 follows a/an.
(a).
distribution with mean and variance equal to
_(b)_
v Choose...
respectively. Fill in the blanks.
(a) normal, (b) 1 and 5
(a) gamma, (b) 1 and 4
X, and X3 are independent. Answer this question with True or False.
1/4
1/2
(a) gamma, (b) 1/2 and 6
(X1 – X2 +1)² follows a/an
(a).
distribution with parameters (b)_
(a) normal, (b) 1 and 7
Fill in the
-
blanks.
(a) gamma, (b) 1 and 7
(a) normal, (b) 2 and 7
(a) gamma, (b) 1/2 and 4
What is the conditional variance of X given (X2, X3) = (1, 1) ?
True
1
3/4
(a) gamma, (b) 1/2 and 8
(a) normal, (b) 2 and 5
TO
Transcribed Image Text:Suppose X has a multivariate normal distribution given by X1 1 1 2р 0 X = X2 · N3 2p 4 0 X3 3 0 0 9 When p = 0.5 ,answer the following questions. 3X1 – X2 follows a/an. (a). distribution with mean and variance equal to _(b)_ v Choose... respectively. Fill in the blanks. (a) normal, (b) 1 and 5 (a) gamma, (b) 1 and 4 X, and X3 are independent. Answer this question with True or False. 1/4 1/2 (a) gamma, (b) 1/2 and 6 (X1 – X2 +1)² follows a/an (a). distribution with parameters (b)_ (a) normal, (b) 1 and 7 Fill in the - blanks. (a) gamma, (b) 1 and 7 (a) normal, (b) 2 and 7 (a) gamma, (b) 1/2 and 4 What is the conditional variance of X given (X2, X3) = (1, 1) ? True 1 3/4 (a) gamma, (b) 1/2 and 8 (a) normal, (b) 2 and 5 TO
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