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Continuous random variables and the normal distribution — Question 371

Original QCE Vault practice · 6 marks

Q371 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 371 (6 marks)

The density of a continuous random variable is
f(x)={x/4,0≤x≤2,(4−x)/4,2<x≤4,0,otherwise.f(x)=\begin{cases}x/4,&0\leq x\leq2,\\(4-x)/4,&2<x\leq4,\\0,&\text{otherwise}.\end{cases}
Triangular density on [0,4] with peak (2,0.5) and zeros at 0 and 4; density zero outside this interval.
a)
Verify that ff is a valid density.
[2 marks]
b)
Determine P(1≤X≤3)P(1\leq X\leq3) exactly.
[2 marks]
c)
Determine the mean and variance exactly.
[2 marks]
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