# Thread: [SOLVED] Mean and Variance Question...

1. ## [SOLVED] Mean and Variance Question...

Question:
Some of the eggs at a market are sold in boxes of six. The number, $\displaystyle X$, 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) $\displaystyle E(X) = 0.3$
$\displaystyle Var(X) = \sum x_i^2p_i - \mu^2$
$\displaystyle Var(X) = 0.6 - 0.3^2$
$\displaystyle Var(X) = 0.51$

(b) Need Help!

(c) Don't know how to comment

2. (b) same as (a) just with 1-X
(c) can you comment now?

3. Originally Posted by Peritus
(b) same as (a) just with 1-X
(c) can you comment now?
But in the textbook, the answer for b is $\displaystyle E(X) = 5.7$ , $\displaystyle Var(x) = 0.51$

4. sorry a typo: the same with the complementing probabilities 1-p:

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