A family buys two policies from the same insurance company...

Name: a family buys two policies from the same insurance company losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10 one policy has 37335
Uploaded: 2023-08-04T03:48:32-08:00
Duration: 5 min 5 s
Channel: Madhur L
Description: a family buys two policies from the same insurance company losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10 one policy has 37335

A family buys two policies from the same insurance company. Losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10. One policy has a deductible of 1 and the other has a deductible of 2. The family experiences exactly one loss under each policy. Calculate the probability that the total benefit paid to the family does not exceed 5. A) 0.13 B) 0.25 C) 0.30 D) 0.32 E) 0.42

Transcript

00:01 Hello students, according to the given question from the given information the total benefit the total benefit paid to the family paid to the family is 0 for if x less than or equal to 1 and y less than or equal to 2 and x minus 1 if x greater than 1 and y less than or equal to 2 and y minus 2 if x is less than or equal to 1 and y greater than 2 and x minus 1 in plus y minus 2 it is if x less than or equal to 1 and y less than or equal to 2.

00:48 So this is equal to x plus y minus 3.

00:51 So here the benefit paid the benefit paid is less than 5 if 0 less than 5 if x less than or equal to 1 and y less than or equal to 2 and x minus 1 less than 5 if x greater than 1 and y greater than or equal to 2 here it is y is less than or equal to 2 and here y minus 2 less than 5 if x is less than or equal to 1 and y is greater than 2 and the last one that is x plus y minus 3 less than 5 if the x value greater than 1 and y is greater than 2.

01:43 So here the first condition that is 0 less than 5 is true always so the total benefit so the total benefit paid is less than 5 always in the region always in the region where x less than or equal to 1 and y less than or equal to 2 and here the second condition was the second condition that gives benefit gives the benefit less than 5.

02:37 So here where x less than 6 and x greater than 1 and y less than or equal to 2 and the third condition gives third condition gives the benefit that is less than 5.

02:56 So where x y is less than 7 and x less than or equal to 1 and y greater than 2.

03:05 So now the finally the last that is fourth condition fourth condition gives the benefit that is less than 5 here where y less than theta minus x x greater than 1 and y greater than 2...

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