Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance. ii. Find the probability that a randomly selected policy holder has a home deduction of at least K100. iii. Are the random variables Χ and Y independent? Explain your answer.
4 (b)
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 K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for ( ) ,YΧ is given by the following table: Χ Y K100 K250
K0 0.20 0.05
K100 0.10 0.15
K200 0.20 0.30
i.
Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance.
ii.
Find the probability that a randomly selected policy holder has a home deduction of at least K100.
iii.
Are the random variables Χ and Y independent? Explain your answer.
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