1. An investment fund in Turkey uses scenario analysis to estimate the expected return and expected risk of Tupra ( a company whose stock trades in Borsa Istanbul). The fund identifies 4 different possible states for the next six months and estimate the following four expected returns for Vestel also assigning a probability to each state.

State Expected Return in 6 months Probability

Very Good 40% 0.1

Good 25% 0.2

Mediocre 10% 0.5

Bad - 10% -

Note: You must find the probability of the bad state using basic statistical theory

1. Find the expected return of Vestel
2. Find the expected variance of Vestel and the standard deviation of Vestel
3. Find the correlation coefficient of Vestel