• Support PF! Buy your school textbooks, materials and every day products Here!

Statistics - Expected Value

  • Thread starter Peter G.
  • Start date
  • #1
442
0
Hi,

I have to work with Expected Values and I am extremely confused over the following:

In the part of my book that teaches me about Probability Distribution, in order to calculate the Expected Value I have to:

Lets say we toss a coin twice. We can get 0 Heads, 1 Heads or 2 Heads

I then draw a probability distribution table and the expected value is the sum of the product of the number of heads and their respective probabilities.

When I get to the part that I learn about Binomial Distributions, in order to get the expected value all I have to do is multiply n by p whereas n is the number of tries and p the probability of success.

What is the difference between the two methods? When should I use each?

Thanks!
 
Last edited:

Answers and Replies

  • #2
danago
Gold Member
1,122
4
Hi,

I have to work with Expected Values and I am extremely confused over the following:

In the part of my book that teaches me about Probability Distribution, in order to calculate the Expected Value I have to:

Lets say we toss a coin twice. We can get 0 Heads, 1 Heads or 2 Heads

I then draw a probability distribution table and the expected value is the sum of the product of the number of heads and their respective probabilities.

When I get to the part that I learn about Binomial Distributions, in order to get the expected value all I have to do is multiply n by p whereas n is the number of tries and p the probability of success.

What is the difference between the two methods? When should I use each?

Thanks!
The equation for the EV of a binomial distribution is derived from the exact same procedure the you have described (sum the product of the outcomes with their respective probabilities) i.e. if X~Bin(n,p), then:

[tex]E(X)=\sum_{x=0}^{n}xP(X=x)[/tex]

So for any n, you could in fact just draw up a table of outcomes and then continue with how you originally solved it, however that will be a lot more work for large n. It is probably a good exercise to try and actually derive the equation E(X)=np from the equation i have posted above, so you can see for yourself that they are identical.

EDIT:
Have a look at this:

http://amath.colorado.edu/courses/4570/2007fall/HandOuts/binexp.pdf [Broken]

It will show you the derivation. Also keep in mind that this only works for binomial random variables.
 
Last edited by a moderator:

Related Threads on Statistics - Expected Value

  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
897
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
11
Views
889
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
814
Top