1. with A random walk (RW) {Sn}n≥0 is a sum of iid r.v.s X1, X2, · · ·, Xn, · · · n Sn = Σ Xi, n = 1, 2, … …. P(X₁ = a) = p, P(X₁ = b) = 1 − p = q. Find the expectation E[S] and variance var(Sn) of S for any n.
1. with A random walk (RW) {Sn}n≥0 is a sum of iid r.v.s X1, X2, · · ·, Xn, · · · n Sn = Σ Xi, n = 1, 2, … …. P(X₁ = a) = p, P(X₁ = b) = 1 − p = q. Find the expectation E[S] and variance var(Sn) of S for any n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A random walk (RW) {Sn}n>o is a sum of id r.v.s X1, X2, •• , Xn,
with
P(X1 = a) = p, P(X1 = b) = 1 -p= q.
Find the expectation E(Snl and variance var(Sn) of Sn for any n.
![1.
with
A random walk (RW) {Sn}n≥0 is a sum of iid r.v.s X1, X2, · · ·, Xn, · · ·
n
Sn = Σ Xi, n = 1, 2, … ….
P(X₁ = a) = p, P(X₁ = b) = 1 − p = q.
Find the expectation E[S] and variance var(Sn) of S for any n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643c9073-bfc9-41d3-b50c-3b14187fea75%2Fb7353f06-e351-4445-8219-36eb7b943da8%2F1kr90lq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
with
A random walk (RW) {Sn}n≥0 is a sum of iid r.v.s X1, X2, · · ·, Xn, · · ·
n
Sn = Σ Xi, n = 1, 2, … ….
P(X₁ = a) = p, P(X₁ = b) = 1 − p = q.
Find the expectation E[S] and variance var(Sn) of S for any n.
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