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Continuous random variables and the normal distribution — Question 325

Original QCE Vault practice · 7 marks

Q325 · Practice questionTechnology-freeComplex unfamiliar7 marks

QUESTION 325 (7 marks)

A random variable XX has density f(x)=kx+1f(x)=\dfrac{k}{x+1} for 0≤x≤e−10\leq x\leq e-1, and zero otherwise.
Density f(x)=1/(x+1) on [0,e-1], decreasing from height 1, zero outside the support.
a)
Determine kk.
[1 mark]
b)
Determine the exact median.
[2 marks]
c)
Determine E(X)E(X) and Var⁡(X)\operatorname{Var}(X) exactly. You may rewrite the integrands using polynomial division.
[4 marks]
Question linkSyllabus coverage

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