Results 1 to 2 of 2

Math Help - about bernoulli

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    13

    about bernoulli

    Let Z1,Z2,Z3,...Zi be iid bernoulli random variables. Let Y be the first Zi to be 1. Calculate E(Y). I know it's a geometric distribution, then i write, E(Y)=∑ 1 x p x q^(y-1). Z1, Z2 Z3... Zi is a bernoulli distribution, so I think the value of Y to be the fisrt success is "1". however, i just wondering the value of Y is the value of Z1, Z2, Z3... ( 0, 1) or the number of trials to get the first success.. I need an explanation. Thx a lot..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by solskjaer View Post
    Let Z1,Z2,Z3,...Zi be iid bernoulli random variables. Let Y be the first Zi to be 1. Calculate E(Y). I know it's a geometric distribution, then i write, E(Y)=∑ 1 x p x q^(y-1). Z1, Z2 Z3... Zi is a bernoulli distribution, so I think the value of Y to be the fisrt success is "1". however, i just wondering the value of Y is the value of Z1, Z2, Z3... ( 0, 1) or the number of trials to get the first success.. I need an explanation. Thx a lot..
    More properly, Y is the first i such that Z_i=1. Thus it is an integer greater that or equal to 1. As a consequence, E[Y]=\sum_{y=1}^\infty y pq^{y-1}=\cdots=\frac{1}{p}.
    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, 12:06 AM
  2. Bernoulli Family
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 5th 2010, 06:57 AM
  3. bernoulli
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 27th 2010, 08:19 AM
  4. bernoulli
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 5th 2007, 09:35 AM
  5. (Bernoulli's Eq)
    Posted in the Calculus Forum
    Replies: 12
    Last Post: October 16th 2007, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum