- #1
WMDhamnekar
MHB
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How to answer this question $\rightarrow$https://stats.stackexchange.com/q/398321/72126
Hello, I am reproducing the question in the hyperlink given in #1 of this thread so that the viewers of this MHB will conveniently read it.Dhamnekar Winod said:How to answer this question $\rightarrow$https://stats.stackexchange.com/q/398321/72126
steep said:I'd like to see some work from you on these. The third one in particular is extremely common and easy. The first is pretty straightforward if you know how to manipulate MGFs to get a martingale. As for the second one, since $S_n$ is even iff n is even, it should be relatively straight forward to attempt as well.
If I were in your shoes, I would start by writing out definitions and applying them to the third one. My guess is that you have foundational issues related to conditional expectations that are holding you back.
A Check Martingale Sequence is a sequence of random variables that satisfy the martingale property, which states that the expected value of the next random variable in the sequence is equal to the current random variable. This property is often used in probability theory and statistics to model and analyze various processes.
Check Martingale Sequences are often constructed using independent and identically distributed (i.i.d.) random variables. This means that each random variable in the sequence is independent of the others and follows the same probability distribution. This allows for easier analysis and calculation of the expected values in the sequence.
Checking for martingale sequences is important in various fields such as finance, economics, and engineering. It allows for the modeling and analysis of random processes and can be used to make predictions and decisions based on the expected values of the sequence.
To check if a sequence is a Check Martingale Sequence, you need to calculate the expected value of each random variable in the sequence and see if it satisfies the martingale property. This involves using mathematical techniques such as conditional probability and conditional expectation.
While Check Martingale Sequences can provide information about the expected values of a sequence, they cannot be used to predict future events with certainty. This is because the sequence is still subject to randomness and other factors that may affect the outcome. However, they can be used to make informed decisions and assess the likelihood of certain outcomes.