YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
YMR0070, YMR3720 Tõenäosusteooria ja matemaatiline statistika
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22<br />
F (x)<br />
✻<br />
1<br />
✛<br />
✛<br />
✛<br />
O<br />
✛<br />
1<br />
2<br />
✛<br />
3<br />
4<br />
✲<br />
5<br />
x<br />
f(x) = 0, 016 δ(x) + 0, 0256 δ(x − 1) + 0, 1536 δ(x − 2)+<br />
+0, 4096 δ(x − 3) + 0, 4096 δ(x − 4),<br />
g(ω) = 0, 016 + 0, 0256e iω + 0, 1536e 2iω + 0, 4096e 3iω + 0, 4096e 4iω =<br />
= (0, 8e iω + 0, 2) 4 ,<br />
EX = 3, 2, DX = 0, 64, σ = 0, 8, P (X < 3) = 0, 1808.<br />
7.24.<br />
x k 1 2 3 ... n ...<br />
p k 0,6 0,24 0,096 ... 0, 6 · 0, 4 n−1 ...<br />
,<br />
EX = 1<br />
0, 6<br />
0, 4<br />
= 1, (6), DX = = 1, (1), σ ≈ 1, 05,<br />
0, 62 F (x) = 0, 6 · 1(x − 1) + 0, 24 · 1(x − 2) + 0, 096 · 1(x − 3) + ...+<br />
∞∑<br />
+0, 6 · 0, 4 n−1 · 1(x − n) + ... = 0, 6 · 0, 4 k−1 · 1(x − k),<br />
f(x) = 0, 6 ·<br />
k=1<br />
∞∑<br />
0, 4 k−1 δ(x − k), F (2, 5) = 0, 84,<br />
k=1<br />
P (X > 3) = 1 − P (X ≤ 3) = 0, 064.
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