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Continuous random variables and the normal distribution — Question 304

Original QCE Vault practice · 6 marks

Q304 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 304 (6 marks)

A random variable XX has density f(x)=kx2f(x)=kx^2 for 0≤x≤10\leq x\leq1, and zero otherwise.
Density f(x)=3x squared on [0,1], increasing from (0,0) to (1,3), zero outside the support.
a)
Determine kk.
[1 mark]
b)
Determine E(X)E(X) and Var⁡(X)\operatorname{Var}(X) exactly.
[3 marks]
c)
Determine the median exactly.
[2 marks]
Question linkSyllabus coverage

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