[Chapter 7] #5 Conditional expectation

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Hello Jingchen,
I am reading Stochastic calculus from Steven Shreve, I am currently doing Chap 11 Jump process.
I am struggling to see how RV for jumps is constructed in Poisson process
(Compound Poisson process and Compensated Poisson process)

Are you able to make a video on the construction of the RV for jump process?

Kindly suggest any material or videos that you may be aware of.

Thank you

kdpr
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Thank you for the nice video.

In condition expectation o X given Y=y, y is fixed and we sum the conditional probability of X for this constant element y.
I am not clear about the below:
Be it in discrete or in Continuous function, is the result of this conditional expectation calculation in RV X terms or Y terms?
The reason I am asking the above clarification is because in E[E[X/Y]] for the calculating this conditioned expectation you are applying Summation for Y=y E[X/Y=y]* p{Y=y}. I am not clear why you chose RV Y - p{Y=y}?

kdpr
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Hello
Jingchen, Thank you for the video.
I have the following questions
1.In section 'Computing expectation by conditioning' you used p{Y=y}. Can I please understand why you choose random variable (RV) Y and not RV X.
2. Usually when a RV Y=y is taken as fixed we sum (or Integrate) the other RV X. But in this section, you have applied sum ( or integrate ) RV Y itself though it is fixed value. Can I please understand why?
3. Generally, when I take a RV as fixed (here RV Y) and I sum for all value of the other RV X I get solution in terms of RV X. What happens in this section 'Computing expectation by conditioning'?

Kindly help

kdpr
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Thank you so much. I understood very well <3😄

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