probability distribution functions (pdf) of several continuous random variables are provided below. Answer the following for each

(i) Confirm that the pdf is valid. (Hint: Check both conditions; a plot might help) (ii) Find the cumulative distribution function (cdf) of the random variable. (iii) Find the probability that the random variable is greater than 1.2. (iv) Find the expected value of the random variable. b) fx(x)= 5 {0 3 o 4 forxe [0, 2] otherwise 12 for x E [1, 3] otherwise for x e [0.5,1.5] for x e (1.5, 2] otherwise