YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika

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E x (t) = 0, 5t, D x (t) = 0, 25t 2 , K x (t 1 , t 2 ) = 0, 25t 1 t 2 , R x (t 1 , t 2 ) = 1.
7.59.
E x (t) = cos t+1−3t, K x (t 1 , t 2 ) = 4+t 1 t 2 , D x (t) = 4+t 2 , σ x (t) = √ 4 + t 2 ,
R x (t 1 , t 2 ) =
4 + t 1 t 2
√
(4 + t
2
1 )(4 + t 2 2) .
7.60.
E x (t) = cos t + 2 sin t, E x (0) = 1, K x (t 1 , t 2 ) =
= 4t 1 t 2 + 9 sin t 1 sin t 2 − 3(t 1 sin t 2 + t 2 sin t 1 ),
D x (t) = 4t 2 + 9 sin 2 t − 6t sin t, D x (0) = 0.
7.61.
E y (t) = 6t 2 + 3t, K y (t 1 , t 2 ) = 9t 1 t 2 cos t 1 cos t 2 ,
D y (t) = 9t 2 cos 2 t, R y (t 1 , t 2 ) = 1.
7.62.
E y (t) = t cos t + sin t, K y (t 1 , t 2 ) = t 3 1t 3 2, σ y (t) = t 3 , R y (t 1 , t 2 ) = 1.
7.63.
E y (t) = et
t , K y(t 1 , t 2 ) = ( ω2
t 1 t 2
) cos ωt 1 cos ωt 2 , D y (t) = ( ω2
t 2 ) cos2 ωt,
σ y (t) = ( ω t ) cos ωt, R y(t 1 , t 2 ) = sign (t 1 t 2 ).
7.64.
K y (t 1 , t 2 ) = 4t 2 1t 2 2 exp(t 2 1 + t 2 2), D y (t) = 4t 4 exp(2t 2 ), σ y (t) = 2t 2 exp t 2 .