# Multiplying curves

#### Stingery

##### New Member
Hi there!

I want to multiply multiple curves (density distributions, with area under curve = 1).
For each curve, I have the x and y values, but x is identical in each curve.
All y values are < 1 and close to zero.
Thus, when multiplying the values, eventually, I reach zero.

Therefore my question:
How can I multiply (and re-normalize so that the area under the curve again = 1) the curves?

Thanks,
Patrick

#### BGM

##### TS Contributor
Why do you want to multiply them together? Any probabilistic meaning?

Anyway, most of the integrable non-negative function can be normalized as a valid probability density function.

Explicitly, if $$f(x), g(x)$$ are two probability density function, then

$$\frac {f(x)g(x)} {\displaystyle \int_{-\infty}^{+\infty} f(x)g(x)dx}$$

is another probability density function (provided that the integral in the denominator exist, finite and non-zero).

A notable example is that if the support of these densities are disjoint, then their product is identical to zero which is meaningless.