Multiplication rules!

Cynthia is fascinated by the multiplication rule applicable to survival probabilities. She wants to verify her earlier calculated probabilities using this rule. But let's start slowly. What is the probability that she (an 18-year-old) will be alive when she is supposed to graduate from her \(3 + 2\) year bachelor and master program?

Next, you will calculate \(_kp_x\) for \(x\) an 18-year-old female and \(k=1,2,3, \ldots\) What is the probability for an 18-year-old to reach the magic number of 100?

The column qx extracted from life_table has been preloaded. The one-year survival probabilities px have been defined as one minus the mortality rates qx.

This exercise is part of the course

Life Insurance Products Valuation in R

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Exercise instructions

Compute the probability of an 18-year-old to turn 23 using prod() (docs).
Define kpx as the multi-year survival probabilities of an 18-year-old until the age of 100 using cumprod().
Print the probability of an 18-year-old to reach the magic number of 100.
Visualize the multi-year survival probabilities by plotting kpx against a vector from 1 until the length() of kpx.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Calculate the probability that (18) survives 5 more years
___(px[(___):(___)])

# Compute the survival probabilities of (18) until the age of 100
kpx <- ___(px[(___):(___)])

# Extract the probability that (18) survives until the age of 100
___

# Plot the probabilties for (18) to reach the age of 19, 20, ..., 100
plot(___, ___, 
    pch = 20, 
    xlab = "k", 
    ylab = expression(paste(""[k], "p"[18])), 
    main = "Survival probabilities for (18)")

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