Summing Independent Random Variable (SOA Exam P – Probability – Multivariate Random Variables)

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After completing this video you should be able to:

- Calculate probabilities for linear combinations of independent normal random variables.

The sum of independent Poisson distributions is Poisson
The sum of independent Normal distributions is Normal
The difference of independent Normal distributions is Normal

Example 1:

The random variables 𝑁_1 and 𝑁_2 are independent Poisson random variables with means 3 and 2, respectively. Calculate the probability their sum is equal to 4.

Example 2:

A certain brand of refrigerator has a useful life that is normally distributed with mean 10 years and standard deviation 3 years. The useful lives of these refrigerators are independent. Calculate the probability that the total useful life of two randomly selected refrigerators will exceed 1.9 times the useful life of a third randomly selected refrigerator.

Example 3:

The number of hurricanes that will hit a certain house in the next ten years is Poisson distributed with mean 4. Each hurricane results in a loss that is exponentially distributed with mean 1000. Losses are mutually independent and independent of the number of hurricanes. Calculate the variance of the total loss due to hurricanes hitting this house in the next ten years.