Find and show work for: f(1,1) f(2,0) f(0,0)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Topic: Joint probability distributions

Find and show work for:

f(1,1)

f(2,0)

f(0,0)

96
Chapter 3 Random Variables and Probability Distributions
5, it will become clear that the joint probability distribution of Table 3.1 can
be represented by the formula
f(x, y)
Y
=
for x = 0, 1, 2; y = 0, 1, 2; and 0 ≤ x + y ≤ 2.
(b) The probability that (X, Y) fall in the region A is
P[(X, Y) € A] = P(X + Y ≤ 1) = ƒ(0,0) + ƒ(0, 1) + ƒ(1, 0)
3 3 9 9
28 14 28
14*
3
(31) (1) (2_2-y)
(8)
= + +
f(x, y)
0
1
2
Table 3.1: Joint Probability Distribution for Example 3.14
Column Totals
0
3
28
3
=
14
1
28
X
1
9
28
3
14
0
2
3
28
0
0
5
15
3
14 28 28
Row
Totals
15
28
1
28
1
When X and Y are continuous random variables, the joint density function
f(x, y) is a surface lying above the xy plane, and P[(X, Y) € A], where A is any
region in the xy plane, is equal to the volume of the right cylinder bounded by the
base A and the surface.
Transcribed Image Text:96 Chapter 3 Random Variables and Probability Distributions 5, it will become clear that the joint probability distribution of Table 3.1 can be represented by the formula f(x, y) Y = for x = 0, 1, 2; y = 0, 1, 2; and 0 ≤ x + y ≤ 2. (b) The probability that (X, Y) fall in the region A is P[(X, Y) € A] = P(X + Y ≤ 1) = ƒ(0,0) + ƒ(0, 1) + ƒ(1, 0) 3 3 9 9 28 14 28 14* 3 (31) (1) (2_2-y) (8) = + + f(x, y) 0 1 2 Table 3.1: Joint Probability Distribution for Example 3.14 Column Totals 0 3 28 3 = 14 1 28 X 1 9 28 3 14 0 2 3 28 0 0 5 15 3 14 28 28 Row Totals 15 28 1 28 1 When X and Y are continuous random variables, the joint density function f(x, y) is a surface lying above the xy plane, and P[(X, Y) € A], where A is any region in the xy plane, is equal to the volume of the right cylinder bounded by the base A and the surface.
Expert Solution
Step 1

Statistics homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman