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Replaced hand drawn image with latex formula, added source link, clarified question
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When reading the slidesa presentation on "expectation propagation"propagation," I found thea strange formula onfor computing $\text{E}[X]$, which is shown in the yellow block of the attached figure. from a conditional probability:

I could not figure out$$\text{E}[X] = \frac{\int x P(y_i|x) dx}{\int P(y_i|x) dx}$$

Can someone please explain how to get this formula was derived? The source is slide 24 in the presentation linked above.

enter image description here

When reading the slides on "expectation propagation", I found the formula on computing $\text{E}[X]$, which is shown in the yellow block of the attached figure.

I could not figure out how to get this formula.

enter image description here

When reading a presentation on "expectation propagation," I found a strange formula for computing $\text{E}[X]$ from a conditional probability:

$$\text{E}[X] = \frac{\int x P(y_i|x) dx}{\int P(y_i|x) dx}$$

Can someone please explain how this formula was derived? The source is slide 24 in the presentation linked above.

regarding Regarding the formula of using P$\text{P}(Y|X)$ to compute E[X]$\text{E}[X]$

whenWhen reading the slides on "expectation propagation", I found the formula on computing E[X]$\text{E}[X]$, which is shown in the yellow block of the attached figure. 

I could not figure out how to get this formula?.

enter image description here

regarding the formula of using P(Y|X) to compute E[X]

when reading the slides on "expectation propagation", I found the formula on computing E[X], which is shown in the yellow block of the attached figure. I could not figure out how to get this formula?

enter image description here

Regarding the formula of using $\text{P}(Y|X)$ to compute $\text{E}[X]$

When reading the slides on "expectation propagation", I found the formula on computing $\text{E}[X]$, which is shown in the yellow block of the attached figure. 

I could not figure out how to get this formula.

enter image description here

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user3125
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regarding the formula of using P(Y|X) to compute E[X]

when reading the slides on "expectation propagation", I found the formula on computing E[X], which is shown in the yellow block of the attached figure. I could not figure out how to get this formula?

enter image description here