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--- math121b:final [2020/05/05 17:07]
pzhou
+++ math121b:final [2020/05/06 11:26] (current)
pzhou [3. Probability and Statistics (20 pts)]
@@ Line 83: / Line 83: @@
 . (5 pt) Consider a random walk on the real line: at  $t=0$ , one start at  $x=0$ . Let  $S_n$  denote the position at  $t=n$ , then  $S_n = S_{n-1} + X_n$ , where  $X_n = \pm 1$  with equal probability.
   * (3pt) What is the variance of  $S_n$ ?
-  * (2pt) Use Markov inequality, prove that
+  * (2pt) Use Markov inequality, prove that for any  $c > 1$ , we have
     $\P(|S_n| > c \sqrt{n}) \leq 1/c^2$

Lecture Notes