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