Question

Problem 3.2 (10 points) Let $(S_n)_{n \ge 0}$ be the symmetric simple random walk starting in 0 (i.e. $S_0 = 0$) with $p = 0.5$. Compute explicitly the following probabilities: (a) (3 points) $\mathbb{P}_0(S_2 = -2|S_9 = -3)$; (b) (3 points) $\mathbb{P}_0(S_2 \le 0, S_6 = 2, S_8 = 2)$; (c) (4 points) $\mathbb{P}_0(T_2 \le 9)$, where $T_k := \min\{n > 0 : S_n = k\}$.

Name: problem 32 10 points let snn ge 0 be the symmetric simple random walk starting in 0 ie s0 0 with p 05 compute explicitly the following probabilities a 3 points mathbbp0s2 2s9 3 b 3 poi 13221
Uploaded: 2022-05-22T15:12:26-08:00
Duration: 2 min 37 s
Channel: Samriddhi Singh
Description: problem 32 10 points let snn ge 0 be the symmetric simple random walk starting in 0 ie s0 0 with p 05 compute explicitly the following probabilities a 3 points mathbbp0s2 2s9 3 b 3 poi 13221

          Problem 3.2 (10 points) Let $(S_n)_{n \ge 0}$ be the symmetric simple random walk starting in 0 (i.e. $S_0 = 0$) with $p = 0.5$.
Compute explicitly the following probabilities:
(a) (3 points) $\mathbb{P}_0(S_2 = -2|S_9 = -3)$;
(b) (3 points) $\mathbb{P}_0(S_2 \le 0, S_6 = 2, S_8 = 2)$;
(c) (4 points) $\mathbb{P}_0(T_2 \le 9)$, where $T_k := \min\{n > 0 : S_n = k\}$.

problem 32 10 points let snn ge 0 be the symmetric simple random walk starting in 0 ie s0 0 with p 05 compute explicitly the following probabilities a 3 points mathbbp0s2 2s9 3 b 3 poi 13221

Added by Matthew M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Samriddhi Singh

05/22/2022

Step 1

5$. This means that at each step, the walk moves up by 1 with probability 0.5 or down by 1 with probability 0.5. We need to compute three probabilities. Part (a): $\mathbb{P}_0(S_2 = -2|S_9 = -3)$. This is a conditional probability. We know that $S_0 = 0$. For a Show more…

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Problem 3.2 (10 points) Let $(S_n)_{n \ge 0}$ be the symmetric simple random walk starting in 0 (i.e. $S_0 = 0$) with $p = 0.5$. Compute explicitly the following probabilities: (a) (3 points) $\mathbb{P}_0(S_2 = -2|S_9 = -3)$; (b) (3 points) $\mathbb{P}_0(S_2 \le 0, S_6 = 2, S_8 = 2)$; (c) (4 points) $\mathbb{P}_0(T_2 \le 9)$, where $T_k := \min\{n > 0 : S_n = k\}$.