SupposeY1; Y2; Y3; : : : are independent Bernoulli random variables with

P(Yi = 0) = 1 =(1/i!)

P(Yi = 1) = 1=i!

Defining X=Y1+Y2+Y3+...Show that E[x]=e-1

Not to sure how to do this queston, so wondering anyone can help me?

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- February 21st 2013, 03:28 AMwrexlive1Independant Bernoulli Random Varible
SupposeY1; Y2; Y3; : : : are independent Bernoulli random variables with

P(Yi = 0) = 1 =(1/i!)

P(Yi = 1) = 1=i!

Defining X=Y1+Y2+Y3+...Show that E[x]=e-1

Not to sure how to do this queston, so wondering anyone can help me?

- February 21st 2013, 09:00 AMSironRe: Independant Bernoulli Random Varible
Note that the expected value has linear properties which we can use here. Unfortunately I'm confused with your notations. Can you explain what you mean with ? We know that are discrete randiom variables, hence . Finally,

- February 21st 2013, 09:25 AMwrexlive1Re: Independant Bernoulli Random Varible
Sorry there has been a typing error, it should read as

P(Yi = 0) = 1 -(1/i!)

P(Yi = 1) = 1/i! - February 21st 2013, 09:38 AMSironRe: Independant Bernoulli Random Varible