An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are $100 and $250, and for Y are $0, $100 and $200. The joint probability density function for (Χ,Y ) is given by the following table: X Y $100 $250 $0 0.2 0.05 $100 0.1 0.15 $200 0.2 0.3 i. Find the probability for a randomly selected policy holder having a $100 deduction on the auto insurance and a $200 deduction on the home insurance. ii. Find the probability that a randomly selected policy holder has a home deduction of at least $100.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
An insurance company provides customers with both auto and home insurance policies.
For a particular customer, Χ is the deduction on his or her auto policy and Y is the
deduction on the home policy. Possible values of Χ are $100 and $250, and for Y are
$0, $100 and $200. The joint
following table:
| X | ||
| Y | $100 | $250 |
| $0 | 0.2 | 0.05 |
| $100 | 0.1 | 0.15 |
| $200 | 0.2 | 0.3 |
i. Find the probability for a randomly selected policy holder having a $100 deduction on the auto insurance and a $200 deduction on the home insurance.
ii. Find the probability that a randomly selected policy holder has a home deduction
of at least $100.
iii. Are the random variables Χ and Y independent? Explain your answer.
iv. If we look only at those insurance customers selecting the lowest auto mobile
insurance deduction ($100), what is the probability that a randomly selected\
customer will also select the lowest home deduction ($0).
v. Compute the
vi. Compute the
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