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Continuous random variables and the normal distribution — Question 305

Original QCE Vault practice · 5 marks

Q305 · Practice questionTechnology-freeSimple familiar5 marks

QUESTION 305 (5 marks)

The time XX hours until a randomly chosen visitor leaves an exhibit has density f(x)=2−x2f(x)=\dfrac{2-x}{2} for 0≤x≤20\leq x\leq2, and zero otherwise.
Density f(x)=(2-x)/2 on [0,2], decreasing from (0,1) to (2,0), zero outside the support.
a)
Determine P(X<1/2)P(X<1/2) exactly.
[2 marks]
b)
Determine the cumulative distribution function for all real xx.
[3 marks]
Question linkSyllabus coverage

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