Question

following either individuals, or a population, over time enables us to build life tables. such tables highlight rates of birth and death for each stage of life. from the data we have collected over the last few years, what is the probability of a goslin surviving to age three? check the theory pages if you need help. a) lx = (0.13 · 0.10 · 0.09) b) lx = (0.27 · 0.13 · 0.10) c) lx = (0.27 · 0.13) d) lx = (0.27 · 0.13 · 0.10 · 0.09)

Explanation:

Step1: Recall life - table concept

In life - table calculations, the probability of surviving to a certain age is the product of survival probabilities at each previous age interval. Usually, we start with an initial survival probability (often considered as 1 or a non - zero value representing the starting cohort) and multiply by the survival probabilities at each subsequent stage.
Let's assume the initial survival probability (at age 0) is 0.27, then the survival probability from age 0 to age 1 is 0.13, and from age 1 to age 2 is 0.10. To find the probability of surviving to age 3, we multiply these probabilities together.

Step2: Calculate survival probability

The probability of surviving to age 3 is the product of survival probabilities at each stage up to age 3. So, \(l_x=(0.27\times0.13\times0.10)\)

Answer:

B. \(l_x=(0.27\times0.13\times0.10)\)