Finding Mean of Beta Distributed Continous Density function

Question

Let $X ∈ (0,1)$ be beta distributed with β-parameter 10, so the density function is:

$p(x) = 10x^9$

1. How can i find the Mean ?

2. How can i find the Variance?

I'm not sure how properly find the values of this for a beta distribution.

I know how to find the Expected values and Variance for discrete values, and i generally i think i realize the formula for continous variables but with the beta distribution im not sure how the intervals should look on the integrals.

Answer 1

$$E(X)=\int_0^1 10x^{10}dx$$

$$E(X^2)=\int_0^1 10x^{11}dx$$

$$V(X)=E(X^2)-E^2(X)$$

Your $X\sim Beta(10;1)$ thus the mean is $\frac{10}{11}$ and similarly for the variance you get $\frac{10}{11^2\cdot 12}$ but also direct calculation with the integral is easy