# area under a pdf not 1?

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Abhinav 2017-7-20

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?

### 采纳的回答

Star Strider 2017-7-20
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.
##### 5 个评论显示 3更早的评论隐藏 3更早的评论
Star Strider 2017-7-20
Not really. After experimenting a bit, it seems to be a function of the length of ‘x’, so there must be some sort of normalization factor involved. Beyond that, I’m not sure. I’ll think about this and if I come up with anything, I’ll post back.
Abhinav 2017-7-20
Okay.

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