# PDF (Prob. Dens. Func.) of multiplication of two functions

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#### hkBattousai

##### Member

I want to measure power and show it on an LCD display using a microcontroller. The MCU has a A/D convertor with 10-bit resolution. In the picture above, I have calculated and illustrated the PDFs (probability density function) of probability of error (I assumed that the error would have a uniform probability).

Now, I know the PDFs of error functions of both i (the current) and v (the voltage). So, how can I calculate the PDF of error function of power (p = v . i)? Will this function have a uniform PDF too? I know that PDF of sum of two probability functions is the convolution of their respective PDFs, but what about the case of multiplication?

My main purpose is to determine the resolution of my circuit output, in other words, the number of meaningful digits after comma on the LCD screen. But I also wonder the mathematical background of this calculation.

#### HATHA

##### New Member
hi
if you know Δv and Δi then
p=vi so
Δp = {(Δv÷v)² + (Δi÷i)²}^1/2

what do you think?

#### hkBattousai

##### Member
hi
if you know Δv and Δi then
p=vi so
Δp = {(Δv÷v)² + (Δi÷i)²}^1/2

what do you think?
Yeah, with a formula like this, maximum possible error can be calculated easily. But I have another interests in this calculation.

1) I want to know the expected value of the error in power, E[Δp], and its density function. So that I can know what amount of error can occur with what probability.

... But I also wonder the mathematical background of this calculation.

2) Just for curiosity, learn the solution of this particular problem.

#### HATHA

##### New Member
i'm not keen in statistic but try this( see attachment)

#### Attachments

• 20091208162934314.pdf
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