If the probability density function of X is given by n2 for 1<x< 2 fx )...

Question

Question

If the probability density function of X is given by n2 for 1<x< 2 fx ) = 10 elsewhere (a) Find, E[X], E[X2], and E[X3] (b) U

Answer 1

Answer #1

a) The moments here are computed as:

1 1 E(X) = xf ()dt = - dx = Ji Ln(2) Ln2

B(x2 – S Pflade = 1, zarade - Bing

B(x) = { flode = 1, madre de vie

b) The value here is computed as:

E(X3 +3X2 - 2x + 5)
= E(X) +3E(X) - 2E(X) + 5
7 3Ln(2) 92 2Ln(2) Ln(2)

2 * 7+9*3- 2*6 +30Ln(2) 6Ln(2)

= 29 + 30Ln(2) 6Ln(2)

This is the required value here.

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Answer 2

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