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

\begin{equation} E(x) = \frac{\alpha+1}{\alpha+\beta+2} \end{equation}

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

Does every think looks good?


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