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Probability and also Statistics for Engineering and Science, ninth Edition

Authors: Jay L. Devore

ISBN-13: 978-1305251809


See our equipment for inquiry 24E from chapter 3 native Devore's Probability and also Statistics for Engineering and also Science.

You are watching: An insurance company offers its policyholders


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An insurance firm offers its policyholders a number of different premium payment options. Because that a randomly selected policyholder, permit X = the variety of months in between successive payments. The cdf of X is together follows...
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Step 1We are provided with cumulative distribution function:\Step 2: (a)At every step, by subtracting subsequent cumulative circulation function, we can discover probability distribution function.\<\beginarraylp\left( 0 \right) = 0\\p\left( 1 \right) = F\left( 1 \right) - F\left( 0 \right) = 0.3 - 0 = 0.3\\p\left( 2 \right) = 0\\p\left( 3 \right) = F\left( 3 \right) - F\left( 2 \right) = 0.4 - 0.3 = 0.1\\p\left( 4 \right) = F\left( 4 \right) - F\left( 3 \right) = 0.45 - 0.40 = 0.05\\p\left( 5 \right) = 0\\p\left( 6 \right) = F\left( 6 \right) - F\left( 5 \right) = 0.60 - 0.45 = 0.15\\p\left( 6 \right) = 0\\p\left( 7 \right) = 0\\p\left( 8 \right) = 0\\p\left( 9 \right) = 0\\p\left( 10 \right) = 0\\p\left( 11 \right) = 0\\p\left( 12 \right) = F\left( 12 \right) - F\left( 11 \right) = 1 - 0.60 = 0.40\endarray\>Step 3: (b)We have to uncover probability in between x=3 and x= inclusive. This is given by:\<\beginarraylp\left( 3 \le x \le 6 \right) = F\left( 6 \right) - F\left( 2 \right)\\ = 0.60 - 0.30\\ = 0.30\\\endarray\>Therefore, \Step 4: (b)We have to discover probability because that x better than or equal to 4. This is offered by:\<\beginarraylp\left( 4 \le x \right) = F\left( 12 \right) - F\left( 3 \right)\\ = 1 - 0.40\\ = 0.60\endarray\>Therefore, \