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Math for Quantitative Finance

# Variance with Indicator Variables

What is the variance of the number of heads you get from flipping 10 fair coins?

Consider flipping 10 fair coins, and counting the number of consecutive HH pairs. The variance of an indicator variable on a single pair is $$\frac{3}{16}.$$ There are 9 possible pairs.

Which option correctly describes the variance of the total number of consecutive HH pairs?

We can use indicator variables to compute the variance of prices in simple models of stock prices.

On any given day, the price of a stock increases with probability $$\frac13$$ and decrease with probability $$\frac23$$. If I have 5 independent stocks, what is the variance of the number of them that will increase in price on any given day?

On any given day, the price of a stock increases with probability $$\frac13$$ and decrease with probability $$\frac23$$. If I have 5 independent stocks, over the course of three days, what is the variance of the number of stocks whose price will increase on all 3 days?

On any given day, the price of a stock increases with probability $$\frac13$$ and decrease with probability $$\frac23$$. What is the minimum number of stocks I could hold such that the variance of the number that will increase every day for three days is at least 1?

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