MATLAB: Question in the Statistics

statisticstheory

f(x,y)=1 for 0<x,y<1 Let z=xy find E(z)

Best Answer

x and y are independent, so E(z) = E(x)*E(y).

You do not know what E(x) is because all that you are given is the range of x, and nothing about the distribution of x. Likewise with E(y).

If The distribution is Uniform Random, then E() of a uniform random variable is mean() of the range. mean() of 0 to 1 is 1/2.

1/2 * 1/2 gives 1/4

Related Solutions

MATLAB: CDF for Loglogistic distribution

Hello ZC,

They are equivalent. In Matlab

cdf =               e^z / (1+e^z)            % the missing one
pdf = (1/(sigma*x))*e^z / (1+e^z)^2
where
z = (log(x)-mu)/sigma

When you make the substitution (as mentioned in wikipedia, where they use s in place of sigma)

beta = 1/sigma        e^mu = alpha
then
e^z = (x/alpha)^beta

and for wiki,

cdf =              (x/alpha)^beta)   /(1+(x/alpha)^beta) 
pdf = (beta/alpha)*(x/alpha)^(beta-1)/(1+(x/alpha)^beta)^2

MATLAB: How to create a function as the convolution of two functions? Thanks

Hello James,

fune=@(e)(e>=0).*(e<=1);
funz=@(z)(z>=0).*(z<=1);
funezt=@(ez,t)fune(ez-t).*funz(t);
funez=@(ez)integral(@(t)funezt(ez,t),0,2,'ArrayValued',true);   % <--
vecez=0:0.01:2;
vecfunez=funez(vecez);
plot(vecez,vecfunez)

A useful Matlab option.

Best Answer

Related Solutions

MATLAB: CDF for Loglogistic distribution

MATLAB: How to create a function as the convolution of two functions? Thanks

Related Question