PR101 Probability of a stock with given random variables

The cost of a stock at the time n is modeled by the random variable X_n. We know that the collection of stock prices is given by: {X_n} from 0 to infinity. The starting price is modeled by the random variable X_0. We also know that P(X_0=200)=1. The price of the stock at the time n depends only on the stock price at time n-1 in the following way: P(X_n = x_n-1 + 1 | X_n-1 = x_n-1) = p, and P(X_n = x_n-1 – 1 | X_n-1 = x_n-1) = 1-p We also know that P(X_n = x | X_n-1 = x_n-1) = 0, for every x not in {x_n-1 – 1, x_n-1 +1} 1) Determine the probability that X_n = 0 for a given n 2) Determine X_n distribution (not conditional) 3) Determine E[X_n] and Var[X_n] Requirements: Detailed yet understandable

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