# Appendix a to applied probability: directory of m-functions and m  (Page 16/24)

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icalcf.m `[x,y,t,u,px,py,p] = icalcf(X,Y,PX,PY)` is a function version of icalc, which allows arbitrary naming of variables.

```function [x,y,t,u,px,py,p] = icalcf(X,Y,PX,PY)% ICALCF [x,y,t,u,px,py,p] = icalcf(X,Y,PX,PY) Function version of icalc% Version of 5/3/95 % Allows arbitrary naming of variablesx = X; y = Y;px = PX; py = PY;if length(X) ~= length(PX) error(' X and PX of different lengths')elseif length(Y) ~= length(PY) error(' Y and PY of different lengths')end [a,b]= meshgrid(PX,fliplr(PY)); p = a.*b; % Matrix of joint independent probabilities[t,u] = meshgrid(X,fliplr(Y)); % t, u matrices for joint calculations```

icalc3.m Calculation setup for an independent class of three simple random variables.

```% ICALC3 file icalc3.m Setup for three independent rv % Version of 5/15/96% Sets up for calculations for three % independent simple random variables% Uses m-functions rep, elrep, kronf X = input('Enter row matrix of X-values ');Y = input('Enter row matrix of Y-values '); Z = input('Enter row matrix of Z-values ');PX = input('Enter X probabilities '); PY = input('Enter Y probabilities ');PZ = input('Enter Z probabilities '); n = length(X);m = length(Y); s = length(Z);[t,u] = meshgrid(X,Y);t = rep(t,1,s); u = rep(u,1,s);v = elrep(Z,m,n); % t,u,v matrices for joint calculations P = kronf(PZ,kronf(PX,PY'));disp('Use array operations on matrices X, Y, Z,') disp('PX, PY, PZ, t, u, v, and P')```

icalc4.m Calculation setup for an independent class of four simple random variables.

```% ICALC4 file icalc4.m Setup for four independent rv % Version of 5/15/96% Sets up for calculations for four % independent simple random variables% Uses m-functions rep, elrep, kronf X = input('Enter row matrix of X-values ');Y = input('Enter row matrix of Y-values '); Z = input('Enter row matrix of Z-values ');W = input('Enter row matrix of W-values '); PX = input('Enter X probabilities ');PY = input('Enter Y probabilities '); PZ = input('Enter Z probabilities ');PW = input('Enter W probabilities '); n = length(X);m = length(Y); s = length(Z);r = length(W); [t,u]= meshgrid(X,Y); t = rep(t,r,s);u = rep(u,r,s); [v,w]= meshgrid(Z,W); v = elrep(v,m,n); % t,u,v,w matrices for joint calculationsw = elrep(w,m,n); P = kronf(kronf(PZ,PW'),kronf(PX,PY'));disp('Use array operations on matrices X, Y, Z, W') disp('PX, PY, PZ, PW, t, u, v, w, and P')```

## Calculations for random variables

ddbn.m Uses the distribution of a simple random variable (or simple approximation) to plot a step graph for the distribution function F X .

```% DDBN file ddbn.m Step graph of distribution function % Version of 10/25/95% Plots step graph of dbn function FX from % distribution of simple rv (or simple approximation)xc = input('Enter row matrix of VALUES '); pc = input('Enter row matrix of PROBABILITIES ');m = length(xc); FX = cumsum(pc);xt = [xc(1)-1-0.1*abs(xc(1)) xc xc(m)+1+0.1*abs(xc(m))];FX = [0 FX 1]; % Artificial extension of range and domainstairs(xt,FX) % Plot of stairstep graph hold onplot(xt,FX,'o') % Marks values at jump hold offgrid xlabel('t')ylabel('u = F(t)') title('Distribution Function')```

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i science that studies human behavior as a relationship between ends and scarcity that have alternative uses
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and u
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hello
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