(a) Let (X) be a random variable with a location-scale t distribution with 3 degrees of freedom,...
Question:
(a) Let \(X\) be a random variable with a location-scale t distribution with 3 degrees of freedom, location 100, and scale 10.
i. What is the probability that \(X\) is less than or equal to 110 ?
ii. What is the 0.25 quantile of \(X\) ?
(b) Generate a sample of 1,000 random numbers following the \((3,100,10)\) location-scale t distribution as above.
Make two q-q plots of the sample side by side, one with a t with 3 degrees of freedom as the reference distribution, and one with a standard normal as the reference distribution. Comment on the plots.
(c) Generate a sample of 1,000 random numbers following the \((6,100,10)\) location-scale t distribution.
Make two q-q plots of the sample side by side, one with a t with 6 degrees of freedom as the reference distribution, and one with a standard normal as the reference distribution. Comment on the plots.
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