There are two possible future states. State $1,$ in which the pandemic forces us to go into another lockdown this winter, happens with probability $0\mathrm{.}3.$ State $2,$ in which we continue to progress toward normalcy this winter, happens with probability $0\mathrm{.}7.$ The following table contains the current prices of Zoom and United as well as their possible prices in the two future states. Assume no arbitrage.

$1.$ What are the realized returns on Zoom in states $1$ and $2?[1$ point$]$

$2.$ What is the expected return on Zoom today $($hint: compute return in each state and use the probabilities$)?[1$ point$]$

$3.$ What is the price of a security that pays $$1$ in state $1$ and $$0$ in state $2.[2$ points$]4.$ What is the price of a security that pays $$0$ in state $1$ and $$1$ in state $2.[2$ points$]5.$ What are the state prices in states $1$ and $2?[2$ points$]$

$6.$ Use you answer from part $5$ to compute the price of Amazon stock. $[2$ points$]$