Problem $1-$ States of the World

The price of a stock under different states of the world are given below:

State Price Probability

Growth $10030\%$

Stability $8020\%$

Recession $4020\%$

Crisis $2030\%$

$1.$ Estimate the expected value, the variance and the standard deviation of the stock price.

$2.$ Suppose that due to new information about the firm, your previous predictions are updated

positively by adding $$10$ in each state. Calculate the new expected value, variance and the

standard deviation of the stock price.$$

$3.$ There is a secret plan for a big acquisition deal that can double the stock price in each state.

Calculate the expected value, variance and the standard deviation of the stock price under

this scenario