I am learning about normal distribution and I have this exercise:
If X is a random variable of normal distribution with mean equal to zero, then all its values They are equal? True or false
My attempt:
The mean,median and mode coincide in the normal distribution. So, if the mean $= 0$, then median, mode $=0$, and also the range of the values that a random variable with a normal distribution can take, are: $]0, \frac{1}{\sigma\sqrt{2\pi}}]$ and since the only value for which the mean is $0$ and all the values are equal, is $0$, but the zero is not within the range, therefore it is false.
I want to know if my development is correct or it has only been a coincidence. Thanks in advance.
Huh??? Why would you ever think that?