- #1
Evo8
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Homework Statement
The PDF (probability density function) of a Gaussian variable x is given by.
$$p_x(x)=\frac{1}{C \sqrt{2 \pi}} e^{\frac{-(x-4)^2}{18}}$$
a) Find C
b)find the probability of x≥2 --> ##P(x≥2)##
Homework Equations
$$ \frac{dF_X(x)}{dx} x=P(x<X≤x+Δx)$$
The Attempt at a Solution
So i get stuck on how to solve the above for C. I have an example of a similar problem that my professor did in class but it skips a lot of steps that I need to see to fully understand. It seems like he started with taking the integral of the signal by using an integral table?
In my textbook I do see that the above is a standard of a gaussian or normal probability density. It looks something like this.
$$p_X(x)=\frac{1}{\sqrt{2 \pi}} e^{-x^2}{2}$$
$$F_X(x)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} e^{\frac{-x^2}{2}}dx$$
Any hints on where to start?
Any help is much appreciated! Thank you!