YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
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32<br />
D x (t) = 4 − 3 sin 6t, ei ole statsionaarne.<br />
7.71.<br />
7.72.<br />
E x (t) = sin t, K x (t 1 , t 2 ) = t 1 t 2 + 3 cos(t 1 − t 2 ),<br />
D x (t) = t 2 + 3, E x ( π 2 ) = 1, D x( π 2 ) = (π2 4 ) + 3.<br />
x i 1 2 3 7 10 11 21<br />
m i 3 1 1 2 1 4 1<br />
¯x ≈ 7, 5, s 2 ≈ 34, 6, s ≈ 5, 88, x 0,75 = 11, 6, x 0,95 = 18, 0.<br />
7.73. EX ∈ (112, 9; 118, 1) = l 0,99 .<br />
7.74. 1 − 0, 9544 ≈ 0, 044.<br />
7.75.<br />
x k 2,70 2,85 2,90 3,20 3,25<br />
m k 2 3 4 1 1<br />
¯x ≈ 2, 91, s 2 ≈ 0, 033, s ≈ 0, 182, EX ∈ (2, 76; 3, 06),<br />
DX ∈ (0, 014; 0, 129), σ ∈ (0, 12; 0, 36).<br />
7.76. cov ∗ (X, Y ) = K ∗ x,y = 1, 6533, r ∗ x,y ≈ 0, 953 (tugev korrelatiivne<br />
seos).<br />
7.77. y = 2, 821 + 0, 765x.<br />
7.78. P (X > x α ) = 1 − P (X < x α ) = 0, 75, x 0,75 = 105, 8.<br />
7.79. H 0 : DX = DY, F arvutuslik = 13, 5, F 0,995; 5,6 = 11, 5, kehtib<br />
hüpotees H 1 : DX ≠ DY ehk X <strong>ja</strong> Y dispersioonid ei ole võrdsed.