# Thread: Can we solve this equation with pdf and cdf?

1. ## Can we solve this equation with pdf and cdf?

Dear,
suppose we have,
pdf((x-1)/2)+cdf((x-3)/4)=3
where pdf is a normal probability density function
and cdf is cumulative density function.
How to express x from this equation?
Best,
Milos

2. ## Re: Can we solve this equation with pdf and cdf?

I can't see why you can't compute this (theoretically). Just substitute the values you want to compute at the pdf and cdf. To express x, you just have to rearrange and make x the subject.

Typing up Normal pdf and Normal CDF will take a bit of time. So to get home the message , let me make a fictitious cdf and pdf.

Suppose,

In this example,

So, the task is just to solve:

So, this is just some basic algebra.

Sometimes, you may not be able to solve the equation explicitly, in which case you can resort to numerical methods.

HTH.

3. ## Re: Can we solve this equation with pdf and cdf?

Originally Posted by MilosM
Dear,
suppose we have,
pdf((x-1)/2)+cdf((x-3)/4)=3
where pdf is a normal probability density function
and cdf is cumulative density function.
How to express x from this equation?
Best,
Milos
Your equation won't work, in general, for any normal distribution. For example, simply consider the standard normal distribution.

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