Чепуренко В.А. Учебное пособие по курсу Теория вероятности
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= |
2(1−x)·(2−2x) |
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x(3 − 4x), |
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2(x |
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∞) |
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P (C ) = |
1)2, |
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x = |
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P (Cx) |
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0.5 |
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0.4 |
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0.3 |
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0.2 |
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0.1 |
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0.0 |
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0.0 |
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sin α2 |
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25 x2 sin α |
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P (Dx) = 4 |
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h |
√5 i2√5 |
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P (D ) = 1 |
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−2 1 − 2 |
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= 2√5x − 1 − |
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x (−∞; 0] |
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√5h |
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25 x2, |
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P (Dx) = |
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2√5x |
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2√5 |
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x > |
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[0; 1] |
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A = x > 1 |
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3} |
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B = {x 6 41} |
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AB A \ C A |
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C = {x |
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+ B A |
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B ABC |
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[0; 1] |
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η1 |
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A = {η1 > 2η2} |
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Bx = {η1 6 x} |
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Cx = {η2 6 x} |
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ACx BxCx BxCx BxCx− 21 |
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= ξ > x |
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Dx
x
DX
R
ξ
90o
x x [0; 2πR]
(0, 0) (0, 1) (1, 0) (1, 1)
(ξ, η)
{|ξ − η| < z} {ξη < z} {min(ξ, η) < z} {max(ξ, η) < z}
12 (ξ + η) < z
Ax = {ξ < x} By = {η < y} AxBy
x, y [0, 1] P (AxBy) = P (Ax) P (By) x2 + ξx + η = 0
x2 + (ξ − η) · x + ξ + η = 1
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31 x3 − ξ2x + η = 0 |
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31 x3 − ξ2x + η = 0 |
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AC = b |
BC = a |
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A = {AM < b} B = {BM < a} A + B AB A \ B |
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} |
D = {Mb < Ma} Mb Ma |
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Gx = {α < x} Hy = {Mc < y} α = MAC |
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[0; 1] |
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x − ξ = x |
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4|x2| + 4y2 |
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x2 + y |
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(ξ − 1) x2 + (3ξ − 2) x = 2ξ + 1
0 |
90o |
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45 |
90o |
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2r < a |
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Bk = { |
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k = 2, 3, 4 |
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n→∞ |
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lim |
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n→∞ |
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α (α < π) |
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r1 < r2 |
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x + y > 1 |
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ρ2 = ξ2 + η2 ϕ = arctg ξη |
P ({ρ < x} · {ϕ < y}) |
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ρ ϕ |
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πˆ |
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l > a
d
a
r 2r < a − d
H
r
λ
L
L → ∞
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S
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B (P (B) > 0) |
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P (AB) |
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PB (A) = |
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P (B) |
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PB (A) = P (A) |
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P(AB) |
= P (A) |
P (B) = |
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P(B) |
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P(AB) |
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P(A) |
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A
B
P (AB) = P (A) P (B) .
AB
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B
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P (AB) − P (A) P (B) |
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qP (A) P |
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P (B) P |
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ρA,B = 0
AB
ρA,B [−1; 1]
ρA,B = 1
P (A) = P (B) = P (AB)
ρA,B = −1
P (A) = P B = P AB
ρA,B < 0 PB (A) < P (A) < PB (A)
ρA,B > 0 PB (A) > P (A) > PB (A)
ρA,B = −ρA,B = ρA,B
A1, A2, ..., An
P (AiAj ) = P (Ai) P (Aj)
i, j {1, 2, ..., n} ; (i 6= j)
P (Ai1 Ai2 ...Aik ) =
= P (Ai1 ) P (Ai2 ) · ... · P (Aik ) i1, i2, ..., ik {1, 2, ..., n} .
P |
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Ai! |
= P (A1) PA1 (A2) PA1A2 (A3) · ... · PA1A2...An−1 (An) . |
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PB (A) > 1 − |
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= P (A) + P (B) 1 + P |
A B > P (B) |
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P (AB) = 1−P AB = 1−P A + B = |
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P (B) P (A) = P (B) P |
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P AB = P (B) P (AB) = P (B) |
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A = { |
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} |
} |
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B = { |
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} |
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C = { |
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D = {
k } Ω = A + C + D
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A, C, D |
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AC = BC = AB = |
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P(A) |
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P ¯ |
(A) = |
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P (A) P (D) |
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D |
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P(D) |
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p |
P (D) = |
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P (A) = |
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P ¯ (A) = |
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D |
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