1. Let X be a random variable with mean μ and variance σ . For a...

1. Let X be a random variable with mean μ and variance σ . For a ∈ R, consider the expectation E ((X − a)2)
a) Write E((X −a)2) in terms of a,μ and σ2
b) For which value a is E ((X − a)2) minimal?
c) For the value a from part (b), what is E ((X − a)2)?

2. Suppose I have a group containing the following first- and second-year university students from various countries. The first 3 are male, and the last 4 female:

Name Home country Year

Andrew UK 1

Sebastian Germany 1

Wei China 1

Fiona UK 1

Lea Germany 2

Ajitha UK 1

Sarah UK 2

I choose a student uniformly at random from the group. Events A = ” the student is male” and B = ” the student is from the UK”. What is P(A|B)?

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orchestra answered 1 year ago

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