Given that, a random function, x(t) is framed by a RV, X representing the amplitude of a cosine wave. That is, x(t) = X x cos(wt + r) where (w and r) are constants, t denotes the time-variable and cos(wt + r) is a deterministic function. Further, the RV, X has the following CDF: Fx(X) = 0 in the range (X K) Suppose a transformation y = a x x(t) + b with a and b being constants is exercised. Hence, determine the following: pdf and valid range of y CDF of y from its LB to 75% of UB Value of the first moment (m1 = Ely]) of y Median of y (Hint: Cumulative distribution of the RV up to its median is exactly equal to: 0.5) Does y denote a stationary process? Why? Assume the following numerical values for (a and b) as: (a = 1.1 and b = 2.7) and choose the correct set of answers in the multiple-choices listed Multiple-choices on the answer-set (ii) CDF of (iv) Median (i) pdf and y: (iii) m1 of y Yes/No Choices of y range of y LB - to - = Ely] Why? (0.75 UB) (2/a2) x 3.4779 a x 12.4312x a x No; Ely]: Function 1 (y - b), 0.2830 *cos(wt+r) xcos(wt+r) of, t (2.7 sys 3.8) (2/a2) x 13.2022 x a x 3.3112 Yes; (y -b), 0.2556 xcos(wt+r) xcos(wt+r) Ely]: Deterministic (2.7 sys 3.8) (2/a2) x 3.2490 a x 13.1015 x a x No; 3 (y - b), 0.2856 x cos(wt+r) xcos(wt+r) Ely]: Function of, t (2.7 sys 3.8) (2/a2) x 3.2192 a x No; pdf of x is 12.1667 xax (y - b), 0.2634 * cos(wt+r) not a function of, t. x(t) is xcos(wt+r) (2.7 sys 3.8) deterministic (2/a2) x 3.1486 a x 13.1000x a x No. Ely]: Deterministic 5 (y -b), 0.2641 x cos(wt+r) Function xcos(wt+r) (2.7 sys 3.8) of, t