Losses covered by a flood insurance policy are uniformly distributed on the interval (0,2). The insurer pays the amount of the loss in excess of a deductible d. The probability that the insurer pays at least 1.20 on a random loss is 0.30. Calculate the probability that the insurer pays at least 1.44 on a random loss.

The probability that the insurer pays at least 1.44 on a random loss is 0.18.

Step-by-step explanation:

Let the random variable X represent the losses covered by a flood insurance policy.

The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.

The probability density function of X is:

It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.

That is:

⇒

The deductible d is 0.20.

Compute the probability that the insurer pays at least 1.44 on a random loss as follows:

Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.