You are given the following estimated survival properties and risk sets determined using the Kaplan-Meier method.

Calculate the standard deviation of [math]\hat{S}(25)[/math] using Greenwood's formula.

• 0.0543
• 0.0556
• 0.0579
• 0.0604
• 0.0626

Initially, 50 lives are included in an observation of survival times following a specific medical treatment. You are given excerpted information from the study data in the table below.

Calculate the Nelson-Aalen estimate of [math]S(2)[/math].

• 0.910
• 0.916
• 0.922
• 0.928
• 0.934

Initially, 80 lives are included in an observation of survival times following a specific medical treatment. You are given excerpted information from the study data in the table below.

Calculate the Kaplan-Meier estimate of [math]S(2)[/math].

• 0.931
• 0.952
• 0.960
• 0.969
• 0.972

You are given the following seriatim data on survival times for a group of 12 lives. The superscript + indicates a right-censored value.

[math]25,32^{+}, 35^{+}, 36,40^{+}, 44,48,60,62^{+}, 65,67,70^{+}[/math]

Calculate the standard deviation of the estimate of [math]S(50)[/math] using the Nelson-Aalen estimator.

• 0.1455
• 0.1519
• 0.1547
• 0.1621
• 0.1650

You are doing a mortality study of insureds between ages 60 and 90 . Two specific lives contributed this data to the study:

You assume mortality follows Gompertz law [math]\mu_{x}=B \times c^{x}[/math] and plan to use maximum likelihood estimation.

[math]L[/math] is the log-likelihood function (using natural logs) associated with these two lives.

[math]L^{*}[/math] denotes the value of [math]L[/math] if the Gompertz parameters are [math]B=0.000004[/math] and [math]c=1.12[/math].

Calculate [math]L^{*}[/math].

• -4,67
• -4.53
• -4.39
• -4.25
• -4.11

You are doing a mortality study of insureds between ages 70 and 90 . Two specific lives contributed this data to the study:

You assume mortality follows Gompertz law [math]\mu_{x}=B \times c^{x}[/math] and plan to use maximum likelihood estimation.

[math]L[/math] is the likelihood function associated with these two lives.

[math]L^{*}[/math] denotes the value of [math]L[/math] if the Gompertz parameters are [math]B=0.000003[/math] and [math]c=1.1[/math].

Calculate [math]L^{*}[/math].

• 0.0115
• 0.0131
• 0.0147
• 0.0163
• 0.0179

In a mortality study, the following grouped death data were collected from 100 lives, all studied beginning at age 40 .

There were no terminations other than death.

Calculate [math]\hat{S}_{40}(32)[/math] using the ogive empirical distribution function.

• 0.44
• 0.48
• 0.52
• 0.56
• 0.60

You are given the following data based on 60 lives at time 0 :

Calculate the upper limit of the 80% linear confidence interval for [math]S(21.0)[/math] using the Kaplan Meier estimate and Greenwood's approximation.

• 0.872
• 0.893
• 0.915
• 0.944
• 0.968

A cohort of 100 newborns is observed from birth. During the first year, 10 drop out of the study and one dies at time 1. Eight more drop out during the next six months, then, at time 1.5, three deaths occur.

Calculate [math]\hat{S}(1.5)[/math], the Nelson-Aalen estimator of the survival function, [math]S(1.5)[/math].

• 0.950
• 0.951
• 0.952
• 0.953
• 0.954

In a study of 1,000 people with a particular illness, 200 died within one year of diagnosis. Calculate a 95% (linear) confidence interval for the one-year empirical survival function.

• (0.745,0.855)
• (0.755,0.845)
• (0.765,0.835)
• (0.775,0.825)
• (0.785,0.815)