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In: Computer Science

A random variable (RV), x is distributed with a pdf as follows: fX(x) = [C ×...

A random variable (RV), x is distributed with a pdf as follows:

fX(x) = [C × x × (1 – x)]       0 ≤ x ≤ a            (C and a are constants)

         = 0                                otherwise

Hence, determine the following: (i) C; (ii) cumulative probability of x in the range, [(u × a) ≤ x ≤ (v × a)]; where u and v are fractions; (iii) E[x]; (iv) second moment of x ; and, (v) standard deviation of x. Assume: a = 1, u = 0.5 and v = 0.75

Hence, choose the correct set of answers in the multiple-choices listed:

Multiple-choices on the answer-set

Choices

(i) C

(ii) cdf

[ua ≤ x ≤ va]

(iii) E[x]

(iv) m2

(v) sigma(x)

1

1.5

0.4458

0.75

0.35

0.250

2

1.6

1.3435

0.60

0.55

0.254

3

1.0

0.3438

0.50

0.30

0.224

4

1.0

0.3466

0.51

0.32

0.124

5

0.8

0.1458

0.45

0.22

0.324

Solutions

Expert Solution

venereology answered 5 months ago
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