- #1
WMDhamnekar
MHB
- 376
- 28
- TL;DR Summary
- Finding expectation of the function of a sum of i.i.d. random variables given the 2nd moment of sum of i. i. d. random variables.
My answer:
Is the above answer correct?
I edited my answer to this question. Does it look now correct?Office_Shredder said:I don't think you're handling the conditional part right. Your final answer is supposed to be a function of ##S_n^2## - given a specific value that it ends up being, what is the expected value of the sine?
##S_n= \pm\sqrt{n}## with equal probability ##\frac12 \therefore E(\sin{(S_n)}|S^2_n)=\sin{(S_n=0)}\times \frac12 - \sin{(S_n=0)}\times \frac12 =0##Office_Shredder said:No, I still think you have written meaningless notation.
Try to compute ##E(\sin(S_n) | S_n)## what does this even mean?
The formula for finding the expectation of the function of a sum is E[f(X+Y)] = E[f(X)] + E[f(Y)], where X and Y are random variables and f is a function.
The expectation of the function of a sum involves finding the expectation of a single function applied to the sum of two random variables, while the expectation of a sum of functions involves finding the sum of the expectations of each individual function applied to the random variables.
Yes, the expectation of the function of a sum can still be calculated even if the random variables are not independent. However, the formula may be more complex and may involve the covariance between the two random variables.
The expectation of the function of a sum is commonly used in statistics and probability to analyze and make predictions about the behavior of random variables. It can also be used in fields such as finance and engineering to model and analyze complex systems.
One limitation is that the formula assumes that the random variables are continuous and have a well-defined probability density function. Additionally, the formula may not be applicable if the random variables have a highly skewed distribution or if the function being applied is not well-behaved.