Exercise Lover

March 27, 2007

Exercises C.4-9

Filed under: C.4 — yuhanlyu @ 12:31 pm

Solution Wanted!

Exercises C.4-8

Filed under: C.4 — yuhanlyu @ 12:30 pm

Solution Wanted!

Exercises C.4-7

Filed under: C.4 — yuhanlyu @ 12:16 pm

b(k;n,1/2) = \frac{n!}{k!(n-k)!2^n} \leq \frac{n^n}{k^k(n-k)^{n-k}2^n} = 2^{nH(k/n)-n}

Exercises C.4-6

Filed under: C.4 — yuhanlyu @ 11:47 am

\sum^n_{k=1} \frac{{n \choose k}{n \ choose k}}{2^n2^n} = $\sum^n_{k=1} \frac{{n \choose k}{n \ choose n-k}}{2^n2^n}$ = ${2n \choose n}/4^n$.

Exercises C.4-5

Filed under: C.4 — yuhanlyu @ 4:33 am

No success = (1-1/n)^n = 1/e
Exact one success = {n \choose 1}/n(1-1/n)^{n-1} = 1/e

Exercises C.4-4

Filed under: C.4 — yuhanlyu @ 4:27 am

Solution Wanted!

Exercises C.4-3

Filed under: C.4 — yuhanlyu @ 4:26 am

b(k;n,p) = {n \choose k}p^k(1-p)^{n-k} = {n \choose n-k}p^k(1-p)^{n-k} = b(n-k; n, 1-p)

Exercises C.4-2

Filed under: C.4 — yuhanlyu @ 4:24 am

Let p = {6 \choose 3}/2^6 = 5/16
E[X] = 16/5

Exercises C.4-1

Filed under: C.4 — yuhanlyu @ 4:20 am

\sum^{\infty}_{k=1} (1-p)^{k-1}p = p \sum^{\infty}_{k=0} (1-p)^k = 1

Blog at WordPress.com.