## Interview Question 2: Central Limit Theorem

1 Q: Roll 100 dice together, what is the probability that the sum of all dice is 400? A Central Limit Theorem: Let $$X_1, X_2,... X_n$$ be independent and identically distributed random variables. The sum of these random variables approaches a normal distribution as $$n \rightarrow \infty$$ $$\sum_{i=1}^n X_i \sim N(n \cdot \mu, n \cdot \sigma^2)$$ , where $$\mu = E[X_i]$$ and $$\sigma^2 = Var(X_i)$$. Let $$X$$ be the value of a die.

## Interview Question 1: Expectations

1 Given a deck of 52 cards, only consider the color black and red. Shuffle the cards. Define that a group is a sequence of same-color cards. For example, Red/Black/Black/Black/Red/Red is an array of 3 groups. Q: What is the expected number of groups? A: Consider a simple case of 2 cards. If they have the same color, the $$E$$ will be 1. $$E$$ will be 2 if the 2 cards have different colors.