Results 1 to 2 of 2

Math Help - bernoulli

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    bernoulli

    given that f is a bernoulli random variable with parameter p=0.3, what is expectation and variance of f?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by alexandrabel90 View Post
    given that f is a bernoulli random variable with parameter p=0.3, what is expectation and variance of f?
    Call that random variable X, then you have

    \mathrm{E}(X)=0\cdot\mathrm{P}(X=0)+1\cdot \mathrm{P}(X=1)=p

    And the variance is

    \mathrm{var}(X)=\mathrm{E}(X^2)-\mathrm{E}^2(X)=p-p^2=p(1-p)

    Where the value of \mathrm{E}(X^2) is p as well, because X^2 still is the same random variable (in this particular case).

    Maybe you are wondering why \mathrm{var}(X)=\mathrm{E}(X^2)-\mathrm{E}^2(X) should be true? That's because

    \mathrm{var}(X)=\mathrm{E}((X-\mathrm{E}(X))^2)=\mathrm{E}(X^2)-2\mathrm{E}^2(X)+\mathrm{E}^2(X)=\ldots

    Don't know why I'm writing this: it's almost certainly to be found in Wikipedia.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. bernoulli
    Posted in the Differential Equations Forum
    Replies: 18
    Last Post: February 22nd 2011, 01:06 AM
  2. Bernoulli Family
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 5th 2010, 07:57 AM
  3. about bernoulli
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 6th 2008, 11:58 PM
  4. bernoulli
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 5th 2007, 10:35 AM
  5. (Bernoulli's Eq)
    Posted in the Calculus Forum
    Replies: 12
    Last Post: October 16th 2007, 03:51 PM

Search Tags


/mathhelpforum @mathhelpforum