# Appendix AList of Problems

This part of the Appendix shows the problems formulated in the chapters of this book. If we write ‘calculate’ or ‘determine’ we mean that the operations should be done using R.

1. Problem 1.1

Calculate the value ϕ(z) of the density function of the standard normal distribution for a given value z.
2. Problem 1.2

Calculate the value Φ(z) of the distribution function of the standard normal distribution for a given value z.
3. Problem 1.3

Calculate the value of the density function of the log‐normal distribution whose logarithm has mean equal to `meanlog = 0` and standard deviation equal to `sdlog = 1` for a given value z.
4. Problem 1.4

Calculate the value of the distribution function of the lognormal distribution whose logarithm has mean equal to `meanlog = 0` and standard deviation equal to `sdlog = 1` for a given value z.
5. Problem 1.5

Calculate the P%‐quantile of the t‐distribution with df degrees of freedom and optional non‐centrality parameter `ncp`.
6. Problem 1.6

Calculate the P%‐quantile of the χ2‐distribution with df degrees of freedom and optional non‐centrality parameter `ncp`.
7. Problem 1.7

Calculate the P%‐quantile of the F‐distribution with df1 and df2 degrees of freedom and optional non‐centrality parameter `ncp`.
8. Problem 1.8

Draw a pure random sample without replacement of size n < N from N given objects represented by numbers 1,…, N without replacing the drawn objects. There are M =  possible unordered samples having the same probability p =  to be selected.
9. Problem ...

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