MATLAB: Area under a pdf not 1

convolutionrandom variables

I have convoluted two pdfs. Both of my pdfs are exponential with lambda=10 and 20, respectively. I have used the following code:
    fun1=@(x)exppdf(x,10);
    fun2=@(x)exppdf(x,20);
    x=0:30;
    y=conv(fun(x),fun2(x));
The code above gives the vector y with 61 elements in it. When I used the 'trapz(0:60,y)' function to find the area under the curve y, it gives 0.80 as output. However, the area should be one since y represents a pdf. I suspect that it is due to the error associated with integration via 'trapz'.
But I need to confirm that I am getting a valid pdf. What function can I use instead of trapz. I cannot use the function 'integral', because it requires functional form of convolution output which I don't have.
Any suggestions?

Best Answer

It has approximately unity area:
fun1 = @(x)exppdf(x,10);
fun2 = @(x)exppdf(x,20);
y = @(x) conv(fun1(x),fun2(x));
x = linspace(0, 100);
yint = trapz(y(x))
yint =
       1.0474
It is necessary to bear in mind the support of PDFs. Integrate it over its entire length.
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