1. If A is the complement of an event A relative to sample space S, then prove that P(A)-1- P(A). (2) 2. Prove that the total area under the normal distribution function curve is 1. (3) 3. 200 passengers have made a reservation for an airplane flight. If the probability that a passenger will not show up is 0.01. Find the proba- bility that exactly 3 will not show up. 4. Find the value of A in the following p.d.f of a continuous r.v"x": [A(3x)(3+), 0x3. f(x). = 0, elsewhere. (2) (3) 5. Find the root of the function up to three decimal places by apply- ing any numerical method f(x)= r 2=1.5. 1, taking an initial value (3) dr 6. Evaluate 1+2 using Trapezoidal Rule, for n = 6. (3) 7. If S-10.0, S2-485, 578.8, and (X-X)(Y-F)=28, 768.4, then find Cov(x, y) and Tay (X-X)=159.45, (YY)-7, 767, 660 (2) 8. State the axioms of probability. (2)