Mathematics
Normality is an important assumption for many statistical techniques. A Box Cox transformation is a way to transform non-normal dependent variables into a normal shape. The Box-Cox transformation of the variable y is also indexed by λ, and is defined as
λ usually takes a value between -2 to +2
Reference: An Analysis of Transformations G. E. P. Box and D. R. Cox Journal of the Royal Statistical Society. Series B (Methodological) Vol. 26, No. 2 (1964), pp. 211-252 https://www.ime.usp.br/~abe/lista/pdfQWaCMboK68.pdf
Given a random generator that produces a number 1 to 5 uniformly, write a function that produces a number from 1 to 7 uniformly.
Assume randX is the function that generates uniform random numbers from 1 to X
rand7 = (rand5 - 1) / 4 * 6 + 1
Once we have a uniform random number from 0 to 1, it can be scaled to any range by multiplying.
Do a inorder traversal of the tree, keep track of the previous element. When inorder traversal ends, the previous element is the second largest.
A fair six-sided die is rolled twice. What is the probability of getting 2 on the first roll and not getting 4 on the second roll?
At first it appear complex but only two dices are rolled there are just 36 possibilities. When first condition is applied positive cases reduces to 6, When 2nd condition is applied positive cases further reduce to 5, so final required probability is 5/36.
The parameters a = min(xi) b = max(xi)
A detailed derivation is given here https://math.stackexchange.com/a/2343976/256094