Let random variable X with the cdf F be uniformly distributed over the union of intervals (0,a) and (a + 2,b). Assuming that F(4) = 0.2 and F(a + 1) = 0.25, find:

(i) a and

b. (ii) F(8.39). (iii) P(3.01 ≤ X ≤ 9.14). (iv) The probability that among 10 values independently selected from this distribution, exactly two will be less than 4 and exactly three will be larger than 17.