Question

If a random variable is Poisson whose mean is 50 claims per month and if these claims are classified as low, medium and high size, and, in addition, we have that the probability of low claim is 0.5, for a medium claim it is 0.4 and for a high claim it is 0.1

Calculate the probability that more than 3 high claims occur in the month.

Answer 1

To calculate the probability of more than 3 high claims in a month for a random variable with a Poisson distribution and a mean of 50 total claims, first determine the mean number of high claims. Then, use the complement rule and the Poisson probability function to find the desired probability.

Step-by-step explanation:

We need to compute the probability that more than 3 high claims occur in a month given a Poisson distribution with a mean of 50 claims per month. Knowing that the probability of a high claim is 0.1, we first find the mean number of high claims per month by multiplying the total mean by this probability, which gives us 5 (50 * 0.1).

Let Y be the random variable representing the number of high claims in a month. Y follows a Poisson distribution with a mean (λ) of 5 (Y ~ Poisson(5)). To find P(Y > 3), we use the complement rule, P(Y > 3) = 1 - P(Y ≤ 3).

Since the probability that Y is 0, 1, 2, or 3 can be found using the Poisson probability function, their sum gives us P(Y ≤ 3). Subtracting this from 1 will give us the probability of having more than 3 high claims in a month.