-
Home
- Applied probability
- Functions of random variables
- Problems on functions of random
(See
Exercise 6 from "Problems on Random Vectors and Joint Distributions", and
Exercise 1 from "Problems on Independent Classes of Random Variables")) The pair
has the joint distribution
(in m-file
npr08_06.m ):
Determine
. Let
.
Determine
and
.
npr08_06 Data are in X, Y, P
jcalcEnter JOINT PROBABILITIES (as on the plane) P
Enter row matrix of VALUES of X XEnter row matrix of VALUES of Y Y
Use array operations on matrices X, Y, PX, PY, t, u, and PP1 = total((max(t,u)<=4).*P)
P1 = 0.4860P2 = total((abs(t-u)>3).*P)
P2 = 0.4516G = 3*t.^3 + 3*t.^2.*u - u.^3;
P3 = total((G<0).*P)
P3 = 0.5420P4 = total(((-5<G)&(G<=300)).*P)
P4 = 0.3713[Z,PZ] = csort(G,P); % Alternate: use dbn for Zp4 = ((-5<Z)&(Z<=300))*PZ'
p4 = 0.3713 Got questions? Get instant answers now!
(See
Exercise 2 from "Problems on Independent Classes of Random Variables") The pair
has the joint distribution (in m-file
npr09_02.m ):
Determine
,
.
npr09_02 Data are in X, Y, P
jcalcEnter JOINT PROBABILITIES (as on the plane) P
Enter row matrix of VALUES of X XEnter row matrix of VALUES of Y Y
Use array operations on matrices X, Y, PX, PY, t, u, and PM1 = (t+u>=5)|(u<=2);
P1 = total(M1.*P)P1 = 0.7054
M2 = t.^2 + u.^2<= 10;
P2 = total(M2.*P)P2 = 0.3282 Got questions? Get instant answers now!
(See
Exercise 7 from "Problems on Random Vectors and Joint Distributions", and
Exercise 3 from "Problems on Independent Classes of Random Variables") The pair
has the joint distribution
(in m-file
npr08_07.m ):
| t = |
-3.1 |
-0.5 |
1.2 |
2.4 |
3.7 |
4.9 |
| u = 7.5 |
0.0090 |
0.0396 |
0.0594 |
0.0216 |
0.0440 |
0.0203 |
| 4.1 |
0.0495 |
0 |
0.1089 |
0.0528 |
0.0363 |
0.0231 |
| -2.0 |
0.0405 |
0.1320 |
0.0891 |
0.0324 |
0.0297 |
0.0189 |
| -3.8 |
0.0510 |
0.0484 |
0.0726 |
0.0132 |
0 |
0.0077 |
Determine
,
.
npr08_07 Data are in X, Y, P
jcalcEnter JOINT PROBABILITIES (as on the plane) P
Enter row matrix of VALUES of X XEnter row matrix of VALUES of Y Y
Use array operations on matrices X, Y, PX, PY, t, u, and PM1 = t.^2 - 3*t<=0;
P1 = total(M1.*P)P1 = 0.4500
M2 = t.^3 - 3*abs(u)<3;
P2 = total(M2.*P)P2 = 0.7876 Got questions? Get instant answers now!
For the pair
in
[link] , let
. Determine and plot the distribution function for
Z .
G = 3*t.^2 + 2*t.*u - u.^2; % Determine g(X,Y)
[Z,PZ]= csort(G,P); % Obtain dbn for Z = g(X,Y)
ddbn % Call for plotting m-procedureEnter row matrix of VALUES Z
Enter row matrix of PROBABILITIES PZ % Plot not reproduced here
Got questions? Get instant answers now!
For the pair
in
[link] , let
Determine and plot the distribution function for
W .
H = t.*(t+u<=4) + 2*u.*(t+u>4);
[W,PW]= csort(H,P);
ddbnEnter row matrix of VALUES W
Enter row matrix of PROBABILITIES PW % Plot not reproduced here
Got questions? Get instant answers now!
For the distributions in Exercises 10-15 below
- Determine analytically the indicated probabilities.
- Use a discrete approximation to calculate the same probablities.'
Questions & Answers
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
Google Play and the Google Play logo are trademarks of Google Inc.
