QCEVault

Continuous random variables and the normal distribution — Question 48

Original QCE Vault practice · 5 marks

Q48 · Practice questionTechnology-activeComplex unfamiliar5 marks

QUESTION 48 (5 marks)

A continuous random variable XX has the triangular density shown, given by f(x)=xf(x)=x for 0≤x≤10\le x\le1 and f(x)=2−xf(x)=2-x for 1<x≤21<x\le2. Determine P(X>1.5∣X>0.5)P(X>1.5\mid X>0.5).
Diagram for question 48
Question linkSyllabus coverage

Related questions

  1. Q8 · Original practice · 1 mark
    A continuous random variable has density f(x)=2xf(x)=2x for 0≤x≤10\le x\le1. Determine P(X>0.6)P(X>0.6).
    Continuous random variables and the normal distribution
  2. Q18 · Original practice · 1 mark
    The random variable XX is normally distributed with mean 80 and standard deviation 5. Determine P(X<85)P(X<85).
    Continuous random variables and the normal distribution
  3. Q33 · Original practice · 2 marks
    A normally distributed variable XX has mean 60 and standard deviation 8. Determine P(X≤68)P(X\le68) to four decimal places.
    Continuous random variables and the normal distribution
  4. Q43 · Original practice · 5 marks
    A normally distributed random variable XX satisfies P(X<42)=0.10P(X<42)=0.10 and P(X<58)=0.90P(X<58)=0.90. Determine the mean and standard deviation of XX to three significant figures.
    Continuous random variables and the normal distribution