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.
Let 𝑋1, 𝑋2, · · · be i.i.d. r.v.s with mean 0, and let 𝑆𝑛 = 𝑋1 + · · · + ⻔
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Let 𝑋1, 𝑋2, · · · be i.i.d. r.v.s with mean 0, and let 𝑆𝑛 = 𝑋1 + · · · + ⻔
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