Computing an expectation

In summary, "Computing an expectation" is a mathematical concept used in statistics and probability to determine the average value of a random variable over a large number of trials. It differs from calculating an average by considering the probability of each outcome. The formula for "Computing an expectation" is E(X) = ∑xP(x), and it has various real-world applications, such as predicting stock market trends and analyzing scientific data. However, its limitations include assuming a uniform distribution of outcomes and not accounting for potential variability.
  • #1
TaPaKaH
54
0
Assume we have a number ##S_0##. For ##i=1..n## define$$S_i=\begin{cases}(1+b)S_{i-1}\text{ with probability }p\\(1+a)S_{i-1}\text{ with probability }1-p\end{cases}$$.
What is the expected value of ##S_n##?
 
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  • #2
Let c = p(1+b) + (1-p)(1+a)

E(Si) = cE(Si-1)

So E(Sn) = cnS0
 

1. What is "Computing an expectation"?

"Computing an expectation" is a mathematical concept used in statistics and probability to determine the average value of a random variable over a large number of trials.

2. How is "Computing an expectation" different from calculating an average?

The main difference between "Computing an expectation" and calculating an average is that "Computing an expectation" takes into account the probability of each outcome, while calculating an average simply sums all values and divides by the number of values.

3. What is the formula for "Computing an expectation"?

The formula for "Computing an expectation" is E(X) = ∑xP(x), where E(X) is the expected value of the random variable X, x is each possible outcome of X, and P(x) is the probability of that outcome occurring.

4. How is "Computing an expectation" used in real-world applications?

"Computing an expectation" is used in many real-world applications, such as predicting stock market trends, analyzing data in scientific experiments, and estimating the average return on a specific investment.

5. Are there any limitations to "Computing an expectation"?

One limitation of "Computing an expectation" is that it assumes a uniform distribution of outcomes, which may not always be the case in real-world scenarios. It also does not take into account the potential variability of outcomes, only the average value.

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