Answer these questions. Please no guess work.

A level assurance is payable immediately on the death of a man aged 40 provided (1) he dies after his 50th birthday, and (2) his death occurs after, but within 15 years of, the death of another life now aged exactly 45. Derive an expression in terms of assurance functions payable on first death for valuing this benefit, assuming that both lives are subject to the same mortality table. [7]The effectiveness of a tablet containing x, my of drug 1 and x2 mg of drug 2 was being tested. In trials the following results were obtained: % effectiveness, y LY 92.5 50.9 20.8 94.9 54.1 16.9 89.3 47.3 25.2 94.1 45.1 49.7 98.9 37.6 95.2 [y= 469.7 Ex, =235 x2 = 207.8 x7 =11,202.68 x =12,886.42 [ xx, = 22, 028.78 _ yx2 =19,870.22 xx2 =8,985.96 (i) Using the multiple linear least square regression model: y = a + Bix+ B212 +e (a) Show that the least squares estimates of a , B, and By satisfy: [xi = na + B, [* + B2Xx12 (b) Hence, using the above data, find their numerical values. [7] (ii) Predict the percentage effectiveness for a tablet containing 51.3 mg of drug x and 18.3 mg of drug x2. [2] [Total 9]