The expected value of Beta Function

Estimate the probability of success

Suppose I send 10 tasks to my machine. 6 out of 10 tasks success, and 4 failed. These outcomes is summarized by $$X$$ as a binary variable, 1 is task success, and 0 if task fail. We know that $$X$$ is continuous random variable

The expected value of a continuous random variable is dependent on the probability density function used to model the probability that the variable will have a certain value. Therefor, I exploit Beta distribution to estimate the probability of success for next tasks. I will $${\alpha}$$ as input of the number past success tasks and $${\beta}$$ as the number of past fail tasks

Expected value

$$$$E(x) = \frac{\alpha+1}{\alpha+\beta+2}$$$$

In my example, $$\alpha = 6$$ and $$\beta = 4$$. Thus, the $$E(x)$$ = 0.58.

Does every think looks good?