(Solved): A random variable (RV), x is distributed with a pdf as follows:   fX(x) = [C x (1 ...

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

 

f_X(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 = 1.15, u = 0.58 and v = 0.86.

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	6.446	0.2838	0.450	0.223	0.141
2	6.570	0.2735	0.451	0.255	0.154
3	6.711	0.2652	0.510	0.231	0.165
4	6.481	0.2877	0.452	0.227	0.150
5	6.802	0.2858	0.455	0.233	0.164

A random variable (RV), \( \mathrm{x} \) is distributed with a pdf as follows: \( f_{x}(x)=[C \times x \times(1-x)] \quad 0 \leq x \leq a \) \( =0 \quad \) otherwise (C and a are constan Hence, determine the following: (i) C; (ii) cumulative probabilit) a)]; where \( u \) and \( v \) are fractions; (iii) \( E[x] \); (iv) second moment of Assume: \( \mathrm{a}=1.15, \mathrm{u}=0.58 \) and \( \mathrm{v}=0.86 \). Hence, choose the correct set of answers in the multiple-choic Multiple-choices on the answer-set