Mathematical expectation, variance, standard deviation?

Question

Mathematics

Tell. The situation is the following.
There is an array A of integers. The array size is 10. The numbers are random in the range from [0 to 100].
Are the statements correct:
1. Expectation + standard deviation <= 100
2. Expectation + variance <= 100
Are there any theorems and proofs to confirm or refute?

Answer 1

oh ... No need for cursing on Habré! You are welcome!
*remembers the deaf blows of himself on the head with Vygodsky's reference book on higher mathematics...

Answer 2

Dispersion D = M(x^2) - M(x)^2 = 3350 - 2500 = 850
Standard deviation s = sqrt(D) = 29.155
Accordingly, 1 - yes, 2 - no.

Answer 3

You just need to familiarize yourself with the basic concepts of probability theory.
Mathematical expectation - in this case, just the average value of the distribution function of a random variable.
Dispersion is a measure of deviation from the mathematical expectation.
The standard deviation is the root of the variance.
Obviously, if the second condition is met, then the first is also satisfied. Your task is simply to understand what variance is and how it is calculated. Here in Wikipedia, for example.
It seems so.