# Indicator Variables

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

# Indicator Variables

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?

# Indicator Variables

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

# Indicator Variables

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?

# Indicator Variables

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?

# Indicator Variables

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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