Minimums and Maximums (SOA Exam P – Probability – Multivariate Random Variables)
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After completing this video you should be able to:
Determine the distribution of order statistics from a set of independent random variables.
𝑀=𝑟𝑣𝑟 the 1^𝑠𝑡 order statistic=𝑚𝑖𝑛(𝑋_1,𝑋_2,⋯,𝑋_𝑛)
𝑀 ̃=𝑟𝑣𝑟 the 𝑛^𝑡ℎ order statistic=𝑚𝑎𝑥(𝑋_1,𝑋_2,⋯,𝑋_𝑛)
For Probabilities involving 𝑀, start with the Survival Function.
For Probabilities involving 𝑀 ̃, start with the Cumulative Distribution Function.
Example:
A random sample of 10 observations from an exponential distribution with mean of 1000 is collected. Determine the probability that the maximum of the observations is greater than 1200.
