Question 5 3.5 pts A random variable (RV), x is exponentially distributed with the parameter, K as follows: fx(x) = K x exp(- Kx) x20 otherwise A transformation of x leads to a new RV, y equal to loge(x), which monotonically increases in the range x 2 0. Hence, determine the following: (i) PDF of y; (ii) range of y; (iii) Cumulative probability distribution of x from its lower-bound (LB) value up to K; (iv) mean value of the RV, x and (v) median of x. Assume K = 3.0. Choose the correct set of answers in the multiple-choices listed: Multiple-choices on the answer-set (iii) CDF of x: (v) Median of Choices (i) PDF of y (ii) Range of y (iv) E[x] LB-to-K X [K x exp(y)] x [exp[-K 1 - * to + * 0.9817 0.1100 0.2146 x exp(y)}] [exp(y)] x 2 - * to 0 0.9945 0.1144 0.2230 [exp(-K2 x exp(y)]] [K x exp(y)] x [exp[-K 3 - * to + * 0.9998 0.1111 0.2311 x exp(y)]] [K x exp(y)] x [exp[-K 4 - * to + * 0.9846 0.1148 0.2621 x exp(y)]] [K x y + exp(y)] + 5 - * to 0 0.9547 0.1125 0.2329 [exp{-K x exp(y)]] O Choice 1 O Choice 2 O Choice 3 O Choice 4 O Choice 5