Begin2.DVI

I11-26.

x f(x) =^9

xe− 9

x!

0 0.00012341

1 0.00111069

2 0.0049981

3 0.0149943

4 0.0337372

5 0.0607269

6 0.0910903

7 0.117116

8 0.131756

9 0.131756

10 0.11858

11 0.0970201

12 0.072765

(a)P(X >4) = 1−

∑ 4

k=0f(k) = 0.^94503636

(b)P(X≤8) =

∑∞

k=0f(k) = 0.^45565260

(c)P(8< X≤12) =

∑ 12

k=8f(k) = 0.^5518747

I11-27. f(k) =^2

ke− 2

k!

(a) f(0) =e−^2 = 0. 1353

(b)

∑∞

k=6

f(k) =1−

∑^5

k=0

f(k) = 0. 0166

(c) 1−

∑^1

k=0

f(k) =0. 5940

I11-28. (a) Write √^1
2 π

∫x

−∞

e−t

(^2) / 2
dt=√^1
2 π
∫ 0
−∞
e−t
(^2) / 2
dt+√^1
2 π
∫x
0
e−t
(^2) / 2
dt
The first integral equals 1/2 and in the second integral make the substitutionτ=t/
√
2
to obtain result.
(b) Similar to part (a) but make the substitutionτ=√^12
(t−μ
σ
)
withdτ=σ√^12 dt.
I11-33. Area≈ 0. 982923
Solutions Chapter 11