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
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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.
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