Výsledky
74.
F(x) =



0 x < 0
p 0 ≤ x < 1
1 x ≥ 1
75.
(a)
p(x) =
1
6 x = 1,2,3,4,5,6
0 jinak.
(b)
F(x) =



0 x < 1
1
6 1 ≤ x < 2
2
6 2 ≤ x < 3
3
6 3 ≤ x < 4
4
6 4 ≤ x < 5
5
6 5 ≤ x < 6
1 x ≥ 6
76.
(a) X ∼ Bi(3, 1
6 )
p(x) =
(3
x)(1
6 )x
(5
6 )3−x
x = 0,1,2,3
0 jinak.
(b) 1
216 = 0.00463
77.
(a)
p(x) =



1
2 x = 0
(1
2 )2
x = 1
(1
2 )3
x = 2
(1
2 )4
x = 3,4
0 jinak.
(b)
F(x) =



0 x < 0
1
2 0 ≤ x < 1
3
4 1 ≤ x < 2
7
8 2 ≤ x < 3
15
16 3 ≤ x < 4
1 x ≥ 4
1
78.
(a)
f (x) =
1
3 3 ≤ x < 6
0 jinak.
80.
(b)
f (x) =
cos(x) 0 ≤ x < π
2
0 jinak.
81.
(b)
F(x) =



0 x < 0
3x2
− 2x3
0 ≤ x < 1
1 x ≥ 1
83.
(b) F(x) = 1
π arctan(x) + 1
2
85.
(b)
f (x) =
e−x
x > 0
0 jinak
92.
p(x, y) =
(9
x)(8
y)( 3
6−x−y) (x, y) ∈ {0,1,...,6}2
3 ≤ x + y ≤ 6
0 jinak
94.
pX (x) =
1
16 (2x2
− 5) x = 2,3
0 jinak
pY (y) =
1
16 (13 − 2y2
) x = 1,2
0 jinak
96.
(b)
F(x, y) =



0 x < 1 ∨ y < 1
(e2
− e)−2
(ey
− e)(ex
− e) x ∈ [1,2] ∧ y ∈ [1,2]
(e2
− e)−1
(ex
− e) x ∈ [1,2] ∧ y > 2
(e2
− e)−1
(ey
− e) x > 2 ∧ y ∈ [1,2]
1 x > 2 ∧ y > 2
2
97.
(b)
F(x, y) =



0 x < 0 ∨ y < 0
(e − 2)−1
(ex y
y − x − 1
y ) x ∈ [0,1] ∧ y ∈ [0,1]
(e − 2)−1
(ex
− x − 1) x ∈ [0,1] ∧ y > 1
(e − 2)−1 ey
y − 1 − 1
y x > 1 ∧ y ∈ [0,1]
1 x > 1 ∧ y > 1
98.
(a) V zadání má být b = 6
(b)
fX (x) =
3
8 x(6 − x) 0 ≤ x ≤ 1
0 jinak
fY (y) =
1
16 (9 − y) 0 ≤ y ≤ 2
0 jinak
99.
(b)
fX (x) =
e−x
x > 0
0 jinak
fY (y) =
e−y
y > 0
0 jinak
(c)
F(x, y) =
(1 − e−y
)(1 − e−x
) x > 0 ∧ y > 0
0 jinak
(d)
FX (x) =
1 − e−x
x > 0
0 jinak
FY (y) =
1 − e−y
y > 0
0 jinak
106.
(a)
F(x, y) =



0 x < 0 ∨ y < 0
1
4 x2
y2
x ∈ [0,1] ∧ y ∈ [0,2]
x2
x ∈ [0,1] ∧ y > 2
1
4 y2
x > 1 ∧ y ∈ [0,2]
1 x > 1 ∧ y > 2
3
(hustota)
f (x, y) =
x y x ∈ [0,1] ∧ y ∈ [0,2]
0 jinak
107.
(a)
FXi
(xi) =



0 xi ≤ 0
x3
i x ∈ (0,1)
1 x ≥ 1
(b) Oznaˇcme FX (x) := FX1
(x1) = FX2
(x2) = FX3
(x3).
3
2
F(0.5)(1 − F(0.5))2
= 0.287
4