Why is the value of the probability function grater than $1$?

Question

Can you explain me, why $P(x)>1$ or why is the value of the function $≈1.2$ ?

$P(x) ≤1$, right?

Answer 1

The figure in the question appears to show graphs of several probability distribution functions. A probability distribution function is not a probability.

In order to convert a probability distribution function into a probability, you can integrate it. The integral can never be greater than $1,$ but the function you are integrating can be greater than $1$ over a small enough interval.

Answer 2

What you see is not $p(x)$, it is $pdf(x),$ which stand for probability density function.

With continuous distributions $p(x)=0$ at every $x$, but $p(a<x<b)$ is the area under the graph of $y=pdf(x)$

Answer 3

$P(x)\le1$, right?

Wrong - what you are thinking of is the fact that for a discrete probability distribution, all probabilities must be at most $1$, since they have to sum to $1$. This is a continuous distribution, so this restriction no longer holds - the sum being equal to $1$ is represented by an integral: $$\int_\Bbb R P(x)\,\mathrm dx=1$$There are no other restrictions on $P$ other than that it is non-negative.