################################################### # Computer Lab 2 – F71SM ################################################### ## In the tasks below, some (but not all) R code is given ## for guidance. In…
F71SM STATISTICAL METHODS 2 PROBABILITY 2.1 Introduction A random experiment is an experiment which is repeatable under identical conditions, and for which, at each repetition,…
F71SM STATISTICAL METHODS 6 SAMPLING DISTRIBUTIONS, CENTRAL LIMIT THEOREM, t and F DISTRIBUTIONS 6.1 Introduction – sampling distributions Let Xi, i = 1,2,…,n be i.i.d.…
F71SM STATISTICAL METHODS 7 ESTIMATION 7.1 Introduction The aim of statistical inference is to extract relevant, useful information from a set of data x =…
F71SM STATISTICAL METHODS Tutorial on Section 4 SPECIAL DISTRIBUTIONS (continuous distributions) 1. LetX∼N(μ,σ2). (a) Show, using the mgf of Z = (X − μ)/σ, that…
F71SM STATISTICAL METHODS Tutorial on Section 7 ESTIMATION 1. Let X = (X1,X2,…,Xn) be a random sample of a gamma r.v. X with pdf f(x)…
F71SM STATISTICAL METHODS Tutorial on Section 3 RANDOM VARIABLES 1. A discrete random variable X has probability mass function x012 f (x) 0.25 0.5 0.25…
F71SM Statistical Methods Heriot-Watt University Computer Lab 1: Data summaries, plots and functions in R 1. The data in this task refer to the amount…
Discrete distributions Uniform on {1, 2, . . . , k}: parameter k a positive integer; X is the outcome in the situation in which…
F71SM STATISTICAL METHODS Tutorial on Section 4 SPECIAL DISTRIBUTIONS (discrete distributions) 1. Let X ∼ b(n,p) and Y ∼ b(n,1−p). Note that P(X ≥ k)…