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  #1  
Old April 14th, 2008, 10:44 AM
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Default [SOLVED] Mean and Variance Question...
Question:
Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table.


(a) Find the expectation and variance of X.
(b) Find the expectation and variance of the number of unbroken eggs in a box.
(c) Comment on the relationship between your answers to part (a) and part (b).

Attempt:


(a) E(X) = 0.3
Var(X) = \sum x_i^2p_i - \mu^2
Var(X) = 0.6 - 0.3^2
Var(X) = 0.51

(b) Need Help!

(c) Don't know how to comment
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Old April 14th, 2008, 11:34 AM
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(b) same as (a) just with 1-X
(c) can you comment now?
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Old April 14th, 2008, 11:39 AM
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Quote:
Originally Posted by Peritus View Post
(b) same as (a) just with 1-X
(c) can you comment now?
But in the textbook, the answer for b is E(X) = 5.7 , Var(x) = 0.51
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Old April 14th, 2008, 11:44 AM
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sorry a typo: the same with the complementing probabilities 1-p:


\sum\limits_i {X\left( {1 - P\left( {X = x_i } \right)} \right)}
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