Let 𝑋1, 𝑋2, · · · be i.i.d. r.v.s with mean 0, and let 𝑆𝑛 = 𝑋1 + · · · + ⻔
Posted: Thu Apr 28, 2022 7:56 am
Let 𝑋1, 𝑋2, · · · be i.i.d. r.v.s with
mean 0, and let 𝑆𝑛 = 𝑋1 + · · ·
+ 𝑋𝑛.
a) Find𝐸(𝑋1 |𝑆𝑛).
b)
Find 𝐸(𝑆𝑘 | 𝑆𝑛) for 1 ≤ 𝑘 ≤ 𝑛.
c) Find 𝐸(𝑆𝑘 | 𝑆𝑛) for 𝑘 > 𝑛.
mean 0, and let 𝑆𝑛 = 𝑋1 + · · ·
+ 𝑋𝑛.
a) Find𝐸(𝑋1 |𝑆𝑛).
b)
Find 𝐸(𝑆𝑘 | 𝑆𝑛) for 1 ≤ 𝑘 ≤ 𝑛.
c) Find 𝐸(𝑆𝑘 | 𝑆𝑛) for 𝑘 > 𝑛.