2020-09-28 20:14:08 +02:00
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#Homework - Sept 27, 2020 - Advanced Multivariate Statistics
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#=============
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#Part.a)
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2020-09-29 16:53:38 +02:00
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f = function(x)
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{
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(x>=0 & x <= 7) * 1/7
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}
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2020-09-28 20:14:08 +02:00
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#(i)
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2020-09-29 16:53:38 +02:00
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integrate(f, lower = -Inf , upper = Inf)
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2020-09-28 20:14:08 +02:00
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#(ii)
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2020-09-29 16:53:38 +02:00
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curve(f, from= -5, to= 12)
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2020-09-28 20:14:08 +02:00
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#(iii)
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#The random variable is X
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#(iv)
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2020-09-29 16:53:38 +02:00
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library(distr6)
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d = distr6::Uniform$new(lower = 0 , upper = 7)
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2020-09-28 20:14:08 +02:00
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d$mgf(t = 1)
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#=============
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#Part.c)
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x1 = c(12,11,8,14,10)
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x2 = c(10,8,5,11,7)
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x3= c(8,11,11,13,6)
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m = matrix(c(x1,x2,x3), ncol = 3)
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vector_means = c(mean(x1), mean(x2), mean(x3))
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vector_means
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cov(m)
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