Kelly makes a series of n bets, each of which she has probability p of winning, independently. Initially, she has x0 dollars. Let Xj be the amount she has immediately after her jth bet is settled. Let f be a constant in (0, 1), called the betting fraction. On each bet, Kelly wagers a fraction f of her wealth, and then she either wins or loses that amount. For example, if her current wealth is $100 and f = 0.25, then she bets $25 and either gains or loses that amount. (A famous choice when p > 1/2 is f = 2p 1, which is known as the Kelly criterion.) Find E(Xn) (in terms of n, p, f, x0). Hint: First find E(Xj+1|Xj )

Statistics: Intro information Data: What is it o information we collect and organize o facts and figures o numbers and text What is the point of Statistics o To process data so that it is useful o Provide meaningful information in an easily accessible way o Answer questions o Tell a story Help business leaders o Improved insight about operations o Make decisions that are: (prove your opinion is right) Data-driven Fact-based o Not based on speculation o EX: UPS, to increase productivity Benefits of Data and Statistics o Reduce cost o Increase profit