How Do Conditional Probabilities and Expectations Relate in Statistics?

  • Thread starter Thread starter MaxManus
  • Start date Start date
  • Tags Tags
    Probability
AI Thread Summary
The discussion focuses on two key statistical concepts: the relationship between conditional probabilities and expectations. The first point involves demonstrating that the probability of Y equaling a specific value can be expressed as a sum of conditional probabilities of Y given X multiplied by the probabilities of X. The second point addresses the expectation of Y, which can be shown to equal the expected value of the conditional expectation of Y given X. Participants emphasize the importance of proper research and understanding of terminology in statistics to solve these problems. Clear communication of mathematical expressions is also highlighted as crucial for effective discussion.
MaxManus
Messages
268
Reaction score
1

Homework Statement


Consider two random variables X and Y. Suppose that Y takes on k values yi,...,yk and X takes l values xi,...,xl

Hey, I am supposed to show that
1) Pr(Y = yi = \sum,from 1 to l Pr(Y = yi(givrn)(X=xi)Pr(X=xi)


and
2) E(Y) = E(E(Y(given)X)


I am not sure where to start on neither of them,
 
Physics news on Phys.org
You need to learn how to do a little research, bro. That second problem is worked out completely on a wikipedia page, which I was able to find in about 20 seconds. I will let you think about what keywords to search for (you should at least know what E(Y) is called). As for the first problem, I'm guessing that you didn't type it in correctly because I can't parse what you're trying to say. Try again?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Getting the probability distribution of a random variable
Replies
2
Views
1K
The joint probability - two coins
Replies
6
Views
2K
Logistic Regression and utility function
Replies
6
Views
2K
I Is this conditional expectation identity true?
Replies
1
Views
2K
How Do You Calculate the Probability of No Events Occurring?
Replies
3
Views
2K
I Help understanding conditional expectation identity
Replies
1
Views
2K
Fortran Need help with Jacobi relaxation method for Dirichlet boundary conditions
Replies
1
Views
1K
Multiplication rule for conditional probabilities
Replies
3
Views
2K
Expected Value of Election Results
Replies
7
Views
1K
Conditional Probability + Poisson Distribution
Replies
14
Views
3K

Hot Threads

Recent Insights

Back
Top