YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
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24<br />
7.34.<br />
f(t) = 0, 1, kui t ∈ [0, 10] <strong>ja</strong> on 0 mu<strong>ja</strong>l, g(ω) = 0, 1(e10ωi − 1)<br />
,<br />
ωi<br />
ET = 5, DT = 25 = 8, (3), 0, 2, 0, 5.<br />
3<br />
7.35.<br />
⎧<br />
⎪⎨ 0, x ≤ 1,<br />
F (x) = (x − 1)<br />
⎪⎩<br />
2 , 1 < x ≤ 2,<br />
1, x > 2<br />
F (x) = (x − 1) 2 (1(x − 1) − 1(x − 2)) + 1(x − 2), EX = 5 3 , DX = 1 18 ,<br />
σ ≈ 0, 24,<br />
5<br />
16 = 0, 3125, 15<br />
16<br />
= 0, 9375<br />
f(x)<br />
✻<br />
2<br />
F (x)<br />
✻<br />
1<br />
O<br />
1<br />
2<br />
✲<br />
x<br />
O<br />
1<br />
2<br />
✲<br />
x<br />
7.36.<br />
F (x) =<br />
{<br />
2 x , x ≤ 0,<br />
1, x > 0,<br />
EX = −1, DX ≈ 3, 16, σ ≈ 1, 8, F (−1) = 0, 5,<br />
P (−2 ≤ X < −1) = 0, 25