7/17/2019 Resumen Variable Aleatoria
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• P (x) = 1
x
• 0 ≤
P (x) ≤
1
x
F (a) = P (x ≤ a)
• P (x ≤ a) = F (a)
• P (x
≥a) = 1
−P (x
≤a) = 1
−F (a)
• P (x < a) =
xi<aP (xi)
µ = [x · P (x)]
σ2 =
(x− µ)2 · P (x)
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X ≈ Bi(n, p)
n
p
P (x) =
n!
(n − x)! · px · q n−x
x = 0, 1, 2, · · · , n
0
x = 0, 1, · · · , n
• n
• x
n
• p
• q
q =
1 − p
F (x) =
0
x < 0
n
x=0
n!
(n − x)! · px · q n−x
x = 0, 1, · · · , n
1
x > n
µ = n · p
σ2 = n · p · q
σ =√
npq
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x
X ≈ P o(µ)
x
P (x) = µx · e−µ
x!
P (x) =
µ · e−µ
x! x = 0, 1, 2, · · · , n
0 x = 0, 1, · · · , n
•
µ
•
σ2 = µ
•
σ =√
µ
n
p
µ
x
0, 1, · · · , n
x
0, 1, 2, · · ·
n
p
n ≥ 100
np ≤ 10
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0
1
1
X ≈ N (0, 1)
z = x− µ
σ
X ≈ N (a, b) ⇒ z = x− µ
σ≈ (0, 1)
np ≥ 5 nq ≥ 5
µ = np
σ =√
npq
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x0 ⇔ X ≥ x0
z = (x0 − 0, 5)− µ
σ
x0 ⇔ X > x0
z = (x0 + 0, 5)
−µ
σ
x0 ⇔ X ≤ x0
z = (x0 + 0, 5)− µ
σ
x0 ⇔ X ≤ x0
z = (x0 − 0, 5)− µ
σ
x0 ⇔ X = x0
x0 − 0, 5 < z < x0 + 5
(x0 − 0, 5)− µ
σ< z <
(x0 + 0, 5)− µ
σ
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