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Zjednodušená ukázka:
Stáhnout celý tento materiála65a56
a80a176a46 a49a46 a83a116a117a100a101a110a116a105 a109a97a106a237 a107a101 a122a107a111a117a178a99a101 a122a97a100a225a110a121 a111a116a225a122a107a121a44 a122 a110a105a99a104a186 a115a105 a112a97a107 a118a121a108a111a115a117a106a237 a106a101a100a110a117a46 a84a121a116a111 a111a116a225a122a107a121 a106a115a111a117 a122a101 a116a176a237
a111a107a114a117a104a183a46 a79a116a225a122a101a107 a122 a112a114a118a110a237a104a111 a111a107a114a117a104a117 a106a101 a115a116a101a106a110a165 a106a97a107a111 a111a116a225a122a101a107 a122 a100a114a117a104a233a104a111 a111a107a114a117a104a117a46 a79a116a225a122a107a121 a122a101 a116a176a101a116a237a104a111
a111a107a114a117a104a117 a116a118a111a176a237 a163a116a118a114a116a105a110a117 a99a101a108a107a111a118a233a104a111 a112a111a163a116a117 a111a116a225a122a101a107a46 a74a97a110a97 a115a101 a110a97a117a163a105a108a97 75% a111a116a225a122a101a107 a122 a112a114a118a110a237a104a111 a111a107a114a117a104a117a44
85% a111a116a225a122a101a107 a122 a100a114a117a104a233a104a111 a111a107a114a117a104a117 a97 50% a111a116a225a122a101a107 a122a101 a116a176a101a116a237a104a111 a111a107a114a117a104a117a46
a97a41 a74a97a107a225 a106a101 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a44 a186a101 a74a97a110a97 a117a100a165a108a225 a122a107a111a117a178a107a117a63
a98a41 a74a97a110a97 a122a107a111a117a178a107a117 a117a100a165a108a97a108a97a46 a74a97a107a225 a106a101 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a44 a186a101 a115a105 a118a121a116a225a104a108a97 a111a116a225a122a107a117 a122a101 a116a176a101a116a237a104a111 a111a107a114a117a104a117a63
a144a101a178a101a110a237a58 a79a122a110a97a163a101a110a237 a106a101a118a183a58 Za46a46a46a74a97a110a97 a117a100a165a108a225 a122a107a111a117a178a107a117a44 Oia46a46a46a111a116a225a122a107a97 a106a101 a122 ia45a116a233a104a111 a111a107a114a117a104a117a46
a90a101 a122a97a100a225a110a237 a112a108a121a110a101a44 a186a101 P(O1) = P(O2)a44 P(O3) = 1/4a46 a77a117a115a237 a112a108a97a116a105a116 P(O1) + P(O2) + P(O3) = 1a44
a116a101a100a121 2P(O1) + 1/4 = 1a46 a79a100a116a117a100 P(O1) = P(O2) = 3/8
a97a41 P(Z) = 38 · 0,75 + 38 · 0,85 + 14 · 0,5 = 0,725.
a98a41 P(O3|Z) = 14·0,5P(Z) .= 0,172 a40a112a176a101a115a110a165 a53a47a50a57a41
a80a176a46 a50a46 a86 a131a101a115a107a233 a114a101a112a117a98a108a105a99a101 a109a225 a112a176a105a98a108a105a186a110a165 42% a108a105a100a237 a107a114a101a118a110a237 a115a107a117a112a105a110a117 a65a44 39% a107a114a101a118a110a237 a115a107a117a112a105a110a117 a48a44 15% a107a114a101a118a110a237
a115a107a117a112a105a110a117 a66 a97 4% a107a114a101a118a110a237 a115a107a117a112a105a110a117 a65a66a46 a78a225a104a111a100a110a165 a118a121a98a101a114a101a109a101 a53 a111a115a111a98a46 a78a225a104a111a100a110a225 a118a101a108a105a163a105a110a97 X a117a100a225a118a225a44
a107a111a108a105a107 a122 a118a121a98a114a97a110a253a99a104 a112a165a116a105 a108a105a100a237 a109a225 a115a107a117a112a105a110a117 a65a46 a86a121a112a111a163a116a165a116a101 a115a116a176a101a100a110a237 a104a111a100a110a111a116a117 a110a225a104a111a100a110a233 a118a101a108a105a163a105a110a121 X a97
a104a111a100a110a111a116a117 a100a105a115a116a114a105a98a117a163a110a237 a102a117a110a107a99a101 a118 a98a111a100a165 x = 3a46
a144a101a178a101a110a237a58 a78a225a104a111a100a110a225 a118a101a108a105a163a105a110a97 X a109a225 a98a105a110a111a109a105a99a107a233 a114a111a122a100a165a108a101a110a237a44 X ∼ Bi(n = 5;p = 0,42)a46 a80a114a111a116a111
EX = n·p = 5 · 0,42 = 2,1 a40a178a108a111 a112a111a163a237a116a97a116 a105 a106a97a107a111 summationtextxi ·p(xi)a44 a97a108a101 a116a111 a98a121 a98a121a108a111 a112a114a97a99a110a233a41a46
F(3) = P(X < 3) = P(X = 0) +P(X = 1) +P(X = 2) = 0,585 + 5 · 0,42 · 0,584+
+parenleftbig52parenrightbig· 0,422 · 0,583 .= 0,647a46
a80a176a46 a51a46 a74a115a111a117 a100a225a110a121 a116a176a105 a102a117a110a107a99a101a58
a97a41 f(x) = (2/9) · (x− 1) a112a114a111 x ∈ 〈1,4〉a44 f(x) = 0 a106a105a110a97a107a44
a98a41 f(x) = x/2 a112a114a111 x ∈ 〈2,4〉a44 f(x) = 0 a106a105a110a97a107a44
a99a41 f(x) = (1/4) · (3 −x) a112a114a111 x ∈ 〈0,4〉a44 f(x) = 0 a106a105a110a97a107a44
a82a111a122a104a111a100a110a165a116a101a44 a107a116a101a114a225 a122 a116a165a99a104a116a111 a102a117a110a107a99a237 a109a183a186a101 a98a253a116 a104a117a115a116a111a116a111a117 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a105 a110a165a106a97a107a233 a110a225a104a111a100a110a233 a118a101a108a105a163a105a110a121
X a21 a122a100a183a118a111a100a110a165a116a101a33 a80a97a107 a118a121a112a111a163a116a165a116a101 P(2,5 < X < 3) a97 P(X > 3,1)a46
a144a101a178a101a110a237a58 a78a97 a111a98a114a225a122a99a237a99a104 a106a115a111a117 a103a114a97a102a121 a118a178a101a99a104 a116a176a237 a102a117a110a107a99a237 a115 a118a121a112a108a110a165a110a111a117 a112a108a111a99a104a111a117 a109a101a122a105 a103a114a97a102a101a109 a97 a111a115a111a117 xa58
0
0.666667
1
2
3
4
5
x
012
1
2
3
4
5
x
0.75 0 –0.25
1
2
3
4
5
x
a97a41 f a106a101 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 f(x) ≥ 0 a97 integraltext∞−∞f(x)dx = 1 a40a110a101a98a111a108a105 a111a98a115a97a104 a118a121a98a97a114a118a101a110a233 a112a108a111a99a104a121 a106a101 1a41
a98a41 f a110a101a110a237 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 a111a98a115a97a104 a112a111a100 a103a114a97a102a101a109 a106a101 a118a165a116a178a237 a110a101a186 1a46
a99a41 f a110a101a110a237 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 a110a97a98a253a118a225 a122a225a112a111a114a110a253a99a104 a104a111a100a110a111a116a46
a83a112a114a225a118a110a225 a104a117a115a116a111a116a97 a116a101a100a121 a106a101 f(x) = (2/9) · (x− 1) a112a114a111 x ∈ 〈1,4〉a46
P(2,5 < X < 3) =
integraldisplay 3
2,5
2
9 · (x− 1)dx =
2
9
bracketleftbiggx2
2 −x
bracketrightbigg3
2,5
= 736 = 0,1944 .= 0,194,
P(X > 3,1) =
integraldisplay 4
3,1
2
9 · (x− 1)dx = 0,51.
a66a56
a80a176a46 a49a46 a83a116a117a100a101a110a116a105 a109a97a106a237 a107a101 a122a107a111a117a178a99a101 a122a97a100a225a110a121 a111a116a225a122a107a121a44 a122 a110a105a99a104a186 a115a105 a112a97a107 a118a121a108a111a115a117a106a237 a106a101a100a110a117a46 a84a121a116a111 a111a116a225a122a107a121 a106a115a111a117 a122a101
a116a176a237 a111a107a114a117a104a183a46 a79a116a225a122a101a107 a122 a112a114a118a110a237a104a111 a111a107a114a117a104a117 a106a101 a100a118a97a107a114a225a116 a118a237a99 a110a101a186 a111a116a225a122a101a107 a122 a100a114a117a104a233a104a111 a111a107a114a117a104a117a46 a79a116a225a122a107a121 a122a101
a116a176a101a116a237a104a111 a111a107a114a117a104a117 a116a118a111a176a237 a116a176a101a116a105a110a117 a99a101a108a107a111a118a233a104a111 a112a111a163a116a117 a111a116a225a122a101a107a46 a74a97a110a97 a115a101 a110a97a117a163a105a108a97 70% a111a116a225a122a101a107 a122 a112a114a118a110a237a104a111
a111a107a114a117a104a117a44 65% a111a116a225a122a101a107 a122 a100a114a117a104a233a104a111 a111a107a114a117a104a117 a97 80% a111a116a225a122a101a107 a122a101 a116a176a101a116a237a104a111 a111a107a114a117a104a117a46
a97a41 a74a97a107a225 a106a101 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a44 a186a101 a74a97a110a97 a117a100a165a108a225 a122a107a111a117a178a107a117a63
a98a41 a74a97a110a97 a122a107a111a117a178a107a117 a117a100a165a108a97a108a97a46 a74a97a107a225 a106a101 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a44 a186a101 a115a105 a118a121a116a225a104a108a97 a111a116a225a122a107a117 a122a101 a100a114a117a104a233a104a111 a111a107a114a117a104a117a63
a144a101a178a101a110a237a58 a79a122a110a97a163a101a110a237 a106a101a118a183a58 Za46a46a46a74a97a110a97 a117a100a165a108a225 a122a107a111a117a178a107a117a44 Oia46a46a46a111a116a225a122a107a97 a106a101 a122 ia45a116a233a104a111 a111a107a114a117a104a117a46
a90a101 a122a97a100a225a110a237 a112a108a121a110a101a44 a186a101 P(O1) = 2P(O2)a44 P(O3) = 1/3a46 a77a117a115a237 a112a108a97a116a105a116 P(O1) +P(O2) +P(O3) = 1a44
a116a101a100a121 3P(O2) + 1/3 = 1a46 a79a100a116a117a100 P(O2) = 2/9a44 P(O1) = 4/9a46
a97a41 P(Z) = 49 · 0,7 + 29 · 0,65 + 13 · 0,8 = 0,722 .= 0,722 a40a112a176a101a115a110a165 a49a51a47a49a56a41
a98a41 P(O2|Z) = 29·0,65P(Z) = 0,2
a80a176a46 a50a46 a86 a131a101a115a107a233 a114a101a112a117a98a108a105a99a101 a109a225 a112a176a105a98a108a105a186a110a165 42% a108a105a100a237 a107a114a101a118a110a237 a115a107a117a112a105a110a117 a65a44 39% a107a114a101a118a110a237 a115a107a117a112a105a110a117 a48a44 15% a107a114a101a118a110a237
a115a107a117a112a105a110a117 a66 a97 4% a107a114a101a118a110a237 a115a107a117a112a105a110a117 a65a66a46 a78a225a104a111a100a110a165 a118a121a98a101a114a101a109a101 a56 a111a115a111a98a46 a78a225a104a111a100a110a225 a118a101a108a105a163a105a110a97 X a117a100a225a118a225a44
a107a111a108a105a107 a122 a118a121a98a114a97a110a253a99a104 a111a115a109a105 a108a105a100a237 a109a225 a115a107a117a112a105a110a117 a66a46 a86a121a112a111a163a116a165a116a101 a115a116a176a101a100a110a237 a104a111a100a110a111a116a117 a110a225a104a111a100a110a233 a118a101a108a105a163a105a110a121 X a97
a104a111a100a110a111a116a117 a100a105a115a116a114a105a98a117a163a110a237 a102a117a110a107a99a101 a118 a98a111a100a165 x = 3a46
a144a101a178a101a110a237a58 a78a225a104a111a100a110a225 a118a101a108a105a163a105a110a97 X a109a225 a98a105a110a111a109a105a99a107a233 a114a111a122a100a165a108a101a110a237a44 X ∼ Bi(n = 8;p = 0,15)a46 a80a114a111a116a111
EX = n·p = 8 · 0,15 = 1,2 a40a178a108a111 a112a111a163a237a116a97a116 a105 a106a97a107a111 summationtextxi ·p(xi)a44 a97a108a101 a116a111 a98a121 a98a121a108a111 a112a114a97a99a110a233a41a46
F(3) = P(X < 3) = P(X = 0) +P(X = 1) +P(X = 2) = 0,858 + 8 · 0,15 · 0,857+
+parenleftbig82parenrightbig· 0,152 · 0,856 .= 0,895a46
a80a176a46 a51a46 a74a115a111a117 a100a225a110a121 a116a176a105 a102a117a110a107a99a101a58
a97a41 f(x) = (2/3) · (x− 1) a112a114a111 x ∈ 〈0,3〉a44 f(x) = 0 a106a105a110a97a107a44
a98a41 f(x) = (1/4) · (x+ 1) a112a114a111 x ∈ 〈0,2〉a44 f(x) = 0 a106a105a110a97a107a44
a99a41 f(x) = 2 −x/2 a112a114a111 x ∈ 〈0,2〉a44 f(x) = 0 a106a105a110a97a107a44
a82a111a122a104a111a100a110a165a116a101a44 a107a116a101a114a225 a122 a116a165a99a104a116a111 a102a117a110a107a99a237 a109a183a186a101 a98a253a116 a104a117a115a116a111a116a111a117 a112a114a97a118a100a165a112a111a100a111a98a110a111a115a116a105 a110a165a106a97a107a233 a110a225a104a111a100a110a233 a118a101a108a105a163a105a110a121
X a21 a122a100a183a118a111a100a110a165a116a101a33 a80a97a107 a118a121a112a111a163a116a165a116a101 P(0,5 < X < 1,5) a97 P(X < 1,8)a46
a144a101a178a101a110a237a58 a78a97 a111a98a114a225a122a99a237a99a104 a106a115a111a117 a103a114a97a102a121 a118a178a101a99a104 a116a176a237 a102a117a110a107a99a237 a115 a118a121a112a108a110a165a110a111a117 a112a108a111a99a104a111a117 a109a101a122a105 a103a114a97a102a101a109 a97 a111a115a111a117 xa58
–0.666667
01.33333
1
2
3
4
x
00.250.75
0.5
1
1.5
2
2.5
x
012
0.5
1
1.5
2
2.5
x
a97a41 f a110a101a110a237 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 a110a97a98a253a118a225 a122a225a112a111a114a110a253a99a104 a104a111a100a110a111a116a46
a98a41 f a106a101 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 f(x) ≥ 0 a97 integraltext∞−∞f(x)dx = 1 a40a110a101a98a111a108a105 a111a98a115a97a104 a118a121a98a97a114a118a101a110a233 a112a108a111a99a104a121 a106a101 1a41
a99a41 f a110a101a110a237 a104a117a115a116a111a116a97a44 a112a114a111a116a111a186a101 a111a98a115a97a104 a112a111a100 a103a114a97a102a101a109 a106a101 a118a165a116a178a237 a110a101a186 1a46
a83a112a114a225a118a110a225 a104a117a115a116a111a116a97 a116a101a100a121 a106a101 f(x) = (1/4) · (x+ 1) a112a114a111 x ∈ 〈0,2〉a46
P(0,5 < X < 1,5) =
integraldisplay 1,5
0,5
1
4 · (x+ 1)dx =
1
4
bracketleftbiggx2
2 +x
bracketrightbigg1,5
0,5
= 12 = 0,5,
P(X < 1,8) =
integraldisplay 1,8
0
1
4 · (x+ 1)dx =
171
200 = 0,855.
a67a56
a8
Vloženo: 28.05.2009
Velikost: 127,89 kB
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