The expected value of Beta Function
$begingroup$
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?
probability expected-value beta-function
asked Jan 7 at 21:35
joujou
12
$endgroup$
add a comment |
$begingroup$
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?
probability expected-value beta-function
asked Jan 7 at 21:35
joujou
12
$endgroup$
add a comment |
$begingroup$
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?
probability expected-value beta-function
asked Jan 7 at 21:35
joujou
12
$endgroup$
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?
probability expected-value beta-function
probability expected-value beta-function
asked Jan 7 at 21:35
joujou
12
asked Jan 7 at 21:35
joujou
12
asked Jan 7 at 21:35
joujou
12
asked Jan 7 at 21:35
joujou
12
asked Jan 7 at 21:35
joujou
12
12
add a comment |
add a comment |
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