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)…
################################################### # Computer Lab 4 – F71SM ################################################### ## In the tasks below, fill in any missing code as ## required. ## Make sure you…
F71SM STATISTICAL METHODS Tutorial on Section 2 PROBABILITY 1. (a) BywritingA∪B∪CasA∪DwhereD=B∪C,verifythat P(A∪B∪C) = P(A)+P(B)+P(C)−P(A∩B)−P(A∩C)−P(B∩C)+P(A∩B∩C) (b) BywritingA∩B∩C asD∩C ,whereD=A∩B,verifythat P(A ∩ B ∩ C) = P(A)P(B|A)P(C|A…