Estimation

PN X
p
p=1
N
N
X
i=1
X(i)
ˆp=30
100 = 30%
= 1,96 ∗p0,3∗0,7/100 = 0,09 = 9% [21%; 39%]
32= 9
pˆp=368
900 = 41%
= 1,96 ∗p0,41 ∗0,59/900 = 0,032 = 3,2% [37,8%; 44,2%]
= 1,96 ∗360/√400 = 35,28
25000 ∗35,28 = 882000
25000 ∗800 = 20000000 [19118000; 20882000]
882000
2000002
= 19,5
400 ∗19,5 = 7800
1,96p0,65 ∗0,35/nini
i

1400/4 = 350
175 ∗1500 = 262500e130 ∗2500 = 325000e
1500 ∗1,97 ∗46/√200 = 9612e2500 ∗1,97 ∗34/√200 = 11840e
[252888e; 272112e] [313160e; 336840e]
1,97 ∗7/√200 = 0,97 1,97 ∗8/√200 = 1,11
[22,03 ; 23,97] [16,89 ; 19,11]
175e130e
1,96 ∗46/√200 = 6,41e1,96 ∗34/√200 = 4,74e
[168,59e; 181,41e] [125,26e; 134,74e]
P={>0}
X
µ=1
5000
5000
X
i=1
X(i)
e e
2,06 ∗63,73/√25 = 26,25e
[138,57e181,07e]
e
n=1,96 ∗63,73
82
= 244

25∗164,82+219∗156,60
244 = 157,44e
25 ∗4062,132 + 219 ∗4920,726
244 = 4832,75
s=√4832,75 = 69,5e
1,96 ∗69,4/√244 = 8,71e[149,63e e ]
5000 ∗157,44 = 787200e
[748150e e ]
n1n2m1m2
(xi)1≤i≤n1(yj)1≤j≤n2
m
n1
X
i=1
(xi−m)2=
n1
X
i=1
((xi−m1)+(m1−m))2=
n1
X
i=1
(xi−m1)2+n1(m1−m)2
Pn1
i=1 (xi−m1) (m1−m)m1
n2
X
j=1
(yj−m)2=
n21
X
j=1
((yj−m2)+(m2−m))2=
n2
X
j=1
(yj−m2)2+n2(m2−m)2
m
s2
n=1
n1+n2−1
n1
X
i=1
(xi−m)2+
n2
X
j=1
(yj−m)2
s2
1=1
n1−1 n1
X
i=1
(xi−m1)2!s2
2=1
n2−1
n2
X
j=1
(yj−m2)2
s2
n=1
n1+n2−1(n1−1) s2
1+n1(m1−m)2+ (n2−1) s2 2+n2(m2−m)2
m
s2
n= 4842,17 s= 69,59
X
P
1500XnXn
1500 ×2304,1 = 3456150
2×753,74/√50 = 210 1500 ×210 = 315000
315000/3456150 = 9,1%
e e n=
(1,96 ×753,74/11,22)2= 17332

D=X−Y
1500×(−11,73) = −17595
2×110,32/√50 = 31,2 1500 ×31,2 = 46800
45735/334890 =
n= (1,96 ×110,32/11,22)2'
371
3366495 −1500 ×3,23 = 3361650
1.96 ×74,734/√371 = 7,60 7,60 ×1500 = 11400
[3350250 ; 3373050]
•228660 + 3361650 + 612750 = 4203060
•4540 + 11400 + 0 = 15940
= 1,96 ×p0,14 (0,86) /371 = 0,035
[10,5% ; 17,5%]