Questions

Chicken and Egg

Recall in the Chicken-Egg problem that we have a chicken that lays eggs, where the number of eggs $N$ follows the distribution $N\sim Pois(\lambda)$. Given that the chicken lays $N$ eggs, the number of eggs that hatch $X$ follows the distribution $X|N \sim Bin(N,p)$.

Q

Find $E(X)$

A

Q

Find $Var(X)$

A

Consumerism

When customers enter a particular store, each makes a purchase with probability $p$, independently. Given that a customer makes a purchase, the amount spent has mean $\mu$ (in dollars) and variance $\sigma^2$.

Q

Find the mean of how much a random customer spends (note that the customer may spend nothing).

A

Q

Find the variance of how much a random customer spends (note that the customer may spend nothing).

A

Trapped Miners

A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him to safety after 3 minutes. The other two doors lead to tunnels that will return him to the mine after 5 and 7 minutes of travel each. The miner is equally likely to choose any of the doors at any time.

Q

What is the expected amount of time until he reaches safety?

A