Few questions about random variables distribution

[Delta]

Hi.

I know that the area under the curve of a probability density function represents probability. But what does y-axis represent in the distribution? And what has mode, median and mean got to do with probability (For e.g the mean = median = mode in normal distribution)

 

[Romsek]

suppose you have a continuous random variable $\displaystyle Y$ distribution with a probability density function $\displaystyle f_Y(x)$

$\displaystyle f_Y(x) = \lim \limits_{\delta \to 0} Pr[x \leq Y < x + \delta]$

You can easily read on the web about mode, median, and mean. I don't need to retype stuff better described elsewhere.

 

[Delta]

suppose you have a continuous random variable $\displaystyle Y$ distribution with a probability density function $\displaystyle f_Y(x)$

$\displaystyle f_Y(x) = \lim \limits_{\delta \to 0} Pr[x \leq Y < x + \delta]$

You can easily read on the web about mode, median, and mean. I don't need to retype stuff better described elsewhere.

But the web doesn't talk about these measures relationship with probability. Like what do they mean when it comes to a distribution of a random variable. (E.g: X~N(1,0) , 0 = stdev, 1 = mean)

 

[pka]

But the web doesn't talk about these measures relationship with probability. Like what do they mean when it comes to a distribution of a random variable. (E.g: X~N(1,0) , 0 = stdev, 1 = mean)

@Delta, You must tell more about yourself and the course in which you are enrolled.
The main thing about your course because your questions imply that the answers require calculus based, set theory based concepts.
Most theoretical based probability courses begin with
Probability Spaces

Probability Spaces
Given any collection of objects, $\displaystyle S$, there is a function, $\displaystyle \mathcal{P}$ which maps the power set, $\displaystyle \mathscr{P}(S)$ of )[the set of all subsets of which are called events] to the number interval $\displaystyle [0,1]$ . The function, $\displaystyle \mathit{P}$ called the probability measure on has three rules:
1) If $\displaystyle A\subseteq S$ then $\displaystyle 0\le \mathcal{P}(A)\le 1$
2) $\displaystyle \mathcal{P}(S)=1$
3) If $\displaystyle \{A,B\}\subseteq\mathscr{P}(S)$ and $\displaystyle A\cap B=\emptyset$ then $\displaystyle \mathcal{P}(A\cup B)=\mathcal{P}(A)+\mathcal{P}(B)$

Those are the general concepts. But then there are three kinds of probability spaces: finite, infinite discrete and continuous.
So tell us about your situation.