please address these carefully

Normal Distribution Property II. Show that if X ~ W(/, a') then for 6 = { - 1, 1}, 6(# - log K) E[max(6(ex - X).0]] = 6etti" 6 (u + 6- - log k) - 5K where K > 0 and 4(.) denotes the cumulative standard normal distribution function.An assurance policy provides a benefit of 1 payable immediately on the death of the last survivor of a male life aged 55 exact and a female life aged 50 exact. Determine: (i) the expected present value of this policy. [4] (ii) the variance of the present value of this policy. [4] Basis: Force of mortality Male life - a constant force of 0.03 Female life a constant force of 0.02 Force of interest [Total 8] A special joint-life deferred annuity policy provides the following benefits: . 20,000 payable immediately on each death at any age a pension payable monthly in advance after 10 years at a rate of 10,000 per annum if both lives are alive and 5,000 per annum if only one life is alive Premiums are payable monthly in advance until the first death for a maximum of 10 years. Show that the monthly premium payable for a male life aged 55 exact and a second female life aged 50 exact is approximately 1,114. Busis: First life mortality PMA92C20 Second life mortality PFA92C20 Rate of interest 4% per annum Expenses Ignore 191