You are given:

(i) [math]\quad S_{0}(t)=\left(1-\frac{t}{\omega}\right)^{\frac{1}{4}}[/math], for [math]0 \leq t \leq \omega[/math]

(ii) [math]\quad \mu_{65}=\frac{1}{180}[/math]

Calculate [math]e_{106}[/math], the curtate expectation of life at age 106 .

• 2.2
• 2.5
• 2.7
• 3.0
• 3.2

Scientists are searching for a vaccine for a disease. You are given:

(i) 100,000 lives age [math]x[/math] are exposed to the disease

(ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1

(iii) The probability that the vaccine will be available is 0.2

(iv) For each life during year [math]1, q_{x}=0.02[/math]

(v) For each life during year 2, [math]q_{x+1}=0.01[/math] if the vaccine has been given, and [math]q_{x+1}=0.02[/math] if it has not been given

Calculate the standard deviation of the number of survivors at the end of year 2.

• 100
• 200
• 300
• 400
• 500

You are given that mortality follows Gompertz Law with [math]B=0.00027[/math] and [math]c=1.1[/math]. Calculate [math]f_{50}(10)[/math].

• 0.048
• 0.050
• 0.052
• 0.054
• 0.056

You are given the survival function:

Calculate [math]1000 \mu_{35}[/math].

• 5.6
• 6.7
• 13.3
• 16.7
• 20.1

You are given the following survival function of a newborn:

Calculate the probability that (30) dies within the next 20 years.

• 0.13
• 0.15
• 0.17
• 0.19
• 0.21

In a population initially consisting of [math]75 \%[/math] females and [math]25 \%[/math] males, you are given:

(i) For a female, the force of mortality is constant and equals [math]\mu[/math]

(ii) For a male, the force of mortality is constant and equals [math]1.5 \mu[/math]

(iii) At the end of 20 years, the population is expected to consist of [math]85 \%[/math] females and [math]15 \%[/math] males

Calculate the probability that a female survives one year.

• 0.89
• 0.92
• 0.94
• 0.96
• 0.99

You are given that mortality follows Makeham's Law with the following parameters:

Let [math]L_{15}[/math] be the random variable representing the number of lives alive at the end of 15 years if there are 10,000 lives age 50 at time 0 .

Calculate [math]\operatorname{Var}\left[L_{15}\right][/math].

• 1,317
• 1,328
• 1,339
• 1,350
• 1,361

You are given:

i)[math] q_{80}=0.04[/math]

ii)[math] q_{81}=0.06[/math]

iii)[math]q_{82}=0.08[/math]

iv) Deaths between ages 80 and 81 are uniformly distributed

v) Deaths between ages 81 and 82 are subject to a constant force of mortality

Calculate the probability that a person aged 80.6 will die between ages 81.1 and 81.6.

• 0.0294
• 0.0296
• 0.0298
• 0.0300
• 0.0302

For a new light bulb, you are given:

i) [math]{ }_{t} q_{0}=\frac{t^{2}+t}{72}[/math] for [math]0 \leq t \leq 8[/math]

ii) [math]T_{0}[/math] is the random variable representing the future lifetime

Calculate [math]\operatorname{Var}\left[T_{0}\right][/math].

• 3.9
• 4.1
• 4.3
• 4.5
• 4.7

You are given the following:

(i) [math] e_{40:20}=18[/math]

(ii) [math]e_{60}=25[/math]

(iii) [math]{ }_{20} q_{40}=0.2[/math]

(iv) [math]q_{40}=0.003[/math]

Calculate [math]e_{41}[/math].

• 36.1
• 37.1
• 38.1
• 39.1
• 40.1