2 | 1 | |||
Oblicz wariancję zmiennej losowej X o gęstości f(x) = | ( | ) | ||
π | ex+e−x |
2 x2 | π2 | |||
∫−∞+∞ | dx = | |||
π(ex+e−x) | 4 |
x2 | x2 e−x | |||
∫−∞+∞ | dx = ∫−∞+∞ | dx = | ||
ex+e−x | 1+e−2x |
x2 e−x | ||
=2 ∫0+∞ | dx = 2 ∫0+∞[x2∑n=0+∞(−1)n e−(2n+1)x] dx = | |
1+e−2x |
(−1)n | ||
= 2 ∑n=0+∞(−1)n∫0+∞[x2 e−(2n+1)x] dx = 4 ∑n=0+∞ | = | |
(2n+1)3 |
π3 | ||
= | ||
8 |
5^2 | 52 |
2^{10} | 210 |
a_2 | a2 |
a_{25} | a25 |
p{2} | √2 |
p{81} | √81 |
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