



(See
Exercise 6 from "Problems on Random Vectors and Joint Distributions", and
Exercise 1 from "Problems on Independent Classes of Random Variables")) The pair
$\{X,\phantom{\rule{0.166667em}{0ex}}Y\}$ has the joint distribution
(in mfile
npr08_06.m ):
$$X=[2.3\phantom{\rule{0.277778em}{0ex}}0.7\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1.1\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}3.9\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}5.1]\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}Y=[1.3\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}2.5\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}4.1\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}5.3]$$
$$P=\left[\begin{array}{ccccc}0.0483\hfill & 0.0357\hfill & 0.0420\hfill & 0.0399\hfill & 0.0441\hfill \\ 0.0437\hfill & 0.0323\hfill & 0.0380\hfill & 0.0361\hfill & 0.0399\hfill \\ 0.0713\hfill & 0.0527\hfill & 0.0620\hfill & 0.0609\hfill & 0.0551\hfill \\ 0.0667\hfill & 0.0493\hfill & 0.0580\hfill & 0.0651\hfill & 0.0589\hfill \end{array}\right]$$
Determine
$P(max\{X,Y\}\le 4),\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}P\left(\rightXY>3)$ . Let
$Z=3{X}^{3}+3{X}^{2}Y{Y}^{3}$ .
Determine
$P(Z<0)$ and
$P(5<Z\le 300)$ .
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(tu)>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
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(See
Exercise 2 from "Problems on Independent Classes of Random Variables") The pair
$\{X,\phantom{\rule{0.166667em}{0ex}}Y\}$ has the joint distribution (in mfile
npr09_02.m ):
$$X=[3.9\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1.7\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1.5\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}2\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}8\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}4.1]\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}Y=[2\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}1\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}2.6\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}5.1]$$
$$P=\left[\begin{array}{ccccc}0.0589\hfill & 0.0342\hfill & 0.0304\hfill & 0.0456\hfill & 0.0209\hfill \\ 0.0961\hfill & 0.0556\hfill & 0.0498\hfill & 0.0744\hfill & 0.0341\hfill \\ 0.0682\hfill & 0.0398\hfill & 0.0350\hfill & 0.0528\hfill & 0.0242\hfill \\ 0.0868\hfill & 0.0504\hfill & 0.0448\hfill & 0.0672\hfill & 0.0308\hfill \end{array}\right]$$
Determine
$P\left(\right\{X+Y\ge 5\}\cup \{Y\le 2\left\}\right)$ ,
$P({X}^{2}+{Y}^{2}\le 10)$ .
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
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(See
Exercise 7 from "Problems on Random Vectors and Joint Distributions", and
Exercise 3 from "Problems on Independent Classes of Random Variables") The pair
$\{X,\phantom{\rule{0.166667em}{0ex}}Y\}$ has the joint distribution
(in mfile
npr08_07.m ):
$$P(X=t,\phantom{\rule{0.277778em}{0ex}}Y=u)$$
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
$P({X}^{2}3X\le 0)$ ,
$P({X}^{3}3Y<3)$ .
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
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For the pair
$\{X,\phantom{\rule{0.166667em}{0ex}}Y\}$ in
[link] , let
$Z=g(X,Y)=3{X}^{2}+2XY{Y}^{2}$ . 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 mprocedureEnter row matrix of VALUES Z
Enter row matrix of PROBABILITIES PZ % Plot not reproduced here
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For the pair
$\{X,\phantom{\rule{0.166667em}{0ex}}Y\}$ in
[link] , let
$$W=g(X,Y)=\left\{\begin{array}{cc}X& \phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\text{for}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}X+Y\le 4\hfill \\ 2Y& \phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\text{for}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}X+Y>4\hfill \end{array}\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}={I}_{M}(X,Y)X+{I}_{{M}^{c}}(X,Y)2Y$$
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
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For the distributions in Exercises 1015 below
 Determine analytically the indicated probabilities.
 Use a discrete approximation to calculate the same probablities.'
Questions & Answers
using the graph illustrate all the types of elascity
Given the budget deficit in recent years, some economists have argued that by adjusting Social Security (SSNIT) payments for inflation using the CPI, SSNIT is overpaying recipients. Discuss the argument being made, and do you agree or disagree with it?
Louis
distinguish between increase in demand curve and extenaion in demamd curve
what are the shapes of an indifference curve?
division of labour is simply the breaking of job functions so that each individual is engage to one set or the other for easy delivery
What is division of labor
it is also simply the breaking down of work into various part so that each individual is entitle to one for easy delivery
EMMANUEL
it is the simplifying of tasks into smaller easily workable divisions where each person specialises on what they understand better
cabs
thanks for your briefing and time
EMMANUEL
What is labour market
Daniel
What is specialisation
Nyaradzai
What is market structure
Peters
What is money and inflation
Peters
What is national income
Peters
what are the sources of monopoly power?
the first source, are informations
amine
political power and influence in monetary institutions
Shahul
what is imperfect competition ?
the situation in which elements of monopoly ( R&D, EOS and stability of prices etc.) allow individual producers or consumers to exercise some control over market prices
Ghulam
where p is less than avc
Koushik
which is the best public finance economics text book?
Shahul
what are the alternatives various of economic system
what is microeconomics
Ayedun
Microeconomics refers to the branch of economics which deals with smaller unit or element of the economy.
Amadu
or Is the study of individual economic unit in a economy..
Neriel
micro economis is the studay of how Households and firms make decision and they interecr it.
mahad
what is financial intermediaries?
financial intermediaries are those who are link between borrowers and lenders for.eg bank... Bank is a financial intermediary
Ajit
why do you here ? why do you want to learn economics
Ajit
والله العظيم انا ماعاوز اتعلمها
انا باخدها غصب عني في الكليه حضرتك
I am student of ecnomics ,
Imran
great, now I am sleeping see u nex time ok
Imran
what is the feature of public ownership of production factors
Toyin
what is the demand for commodity that posses identical utilities called
Toyin
law of diminishing utility...as the quantity consumed of a commodity increases,the utility derived from each successive unit goes on decreasing... condition___ consumption of other commodities remaining the same.
Malik
sorry it's...Law of diminishing marginal utility
Malik
demand for commodities that posses identical utilities?
The commodities having identical utilities are perfect substitutes...and the demand for such type of commodities is called "Competitive Demand".
Malik
Why many people can't differentiate Economists and financial analysts
Hatimu
what is the function of the central bank in an economic?
Toyin
the central bank may lend some money to banks if necessary
konglan
is the study of how societies allocate and manage their scare resources
Neriel
Population is a number of people living in a particular area within a particular time
Rabby
Population is the number of people living in a particular geographical area within a particular time
Rabby
how does this chat work
Dalaya
ya the ideas are good thanks friends
South
so what's the next question?
South
is a tabular representation of the quantity demanded of a particular product at a particular price over a given period of time
Loveth
Difference between extinct and extici spicies
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive
Source:
OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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