Continuous densities and cumulative probabilities

STA 112. Practice questions, not past papers.

Lessons

• Normalise a density
• Move between density and CDF

Practice questions

1. A valid continuous density must have which total area?

   Statistics study edition practice item Q129; Source: T51, T54-55, S18-20, S22-26

2. Which quantity is integrated to find an interval probability?

   Statistics study edition practice item Q130; Source: T51, T54-55, S18-20, S22-26

3. Can a density height exceed 1?

   Statistics study edition practice item Q131; Source: T51, T54-55, S18-20, S22-26

4. Where a continuous CDF is differentiable, its derivative is what?

   Statistics study edition practice item Q132; Source: T51, T54-55, S18-20, S22-26

5. f(x)=k(4x-2x²) on 0<x<2 and zero elsewhere. Find k. Give the value to 4 decimal places.

   Statistics study edition practice item Q133; Source: S19

6. f(x)=x²/9 on 0<x<3 and zero elsewhere. Find P(1<X<2). Give the value to 4 decimal places.

   Statistics study edition practice item Q134; Source: S20

7. f(x)=81x² on 0<x<1/3 and zero elsewhere. Find E(X). Give the value to 4 decimal places.

   Statistics study edition practice item Q135; Source: S22

8. A continuous density integrates to _____ over its full support.

   Statistics study edition practice item F043; Source: T51, T54-55, S18-20, S22-26

9. Differentiating a differentiable CDF gives the _____.

   Statistics study edition practice item F044; Source: T51, T54-55, S18-20, S22-26

Topic gap report