Forahigh-riskdriver, thetimeindaysbetweenthe beginning of a year and an accident has an exponential pdf. suppose an insurance company believes the probability that such a driver will be involved in an accident in the first forty days is 0.25. what is the probability that such a driver will be involved in an accident during the first seventy-five days of the year?

The probability that such a driver will be involved in an accident during the first seventy-five days of the year is 0.408

Step-by-step explanation:

Consider the provide information.

The probability that such a driver will be involved in an accident in the first forty days is 0.25.

Therefore,

Where is X represents the random variable that shows time between beginning of a year and an accident.

X is the exponential distribution with λ as a parameter.

Therefore,

Now we want the probability that a driver will be involved in an accident during the first seventy five days.

Hence, the probability that such a driver will be involved in an accident during the first seventy-five days of the year is 0.408

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