Gamma integrals and distribution

STA 112. Practice questions, not past papers.

Lessons

• Gamma function and normalisation
• Moments and a labelled connection

Practice questions

1. For gamma shape r and rate λ, the mean is what?

   Statistics study edition practice item Q185; Source: S42-44; T74 objective only

2. For a positive integer m, Γ(m) equals what?

   Statistics study edition practice item Q186; Source: S42-44; T74 objective only

3. Which quantity is the scale corresponding to rate λ?

   Statistics study edition practice item Q187; Source: S42-44; T74 objective only

4. Setting gamma shape r=1 gives which distribution?

   Statistics study edition practice item Q188; Source: S42-44; T74 objective only

5. X is gamma with shape 3 and rate 2. Find Var(X). Give the value to 4 decimal places.

   Statistics study edition practice item Q189; Source: S42-44

6. X is gamma with shape 4 and rate 5. Find Var(X). Give the value to 4 decimal places.

   Statistics study edition practice item Q190; Source: S42-44

7. X is gamma with shape 2 and rate 3. Find Var(X). Give the value to 4 decimal places.

   Statistics study edition practice item Q191; Source: S42-44

8. Evaluate the integral of x² exp(-5x) from 0 to infinity. Give the value to 4 decimal places.

   Statistics study edition practice item Q192; Source: S42

9. Gamma rate and scale are _____ of each other.

   Statistics study edition practice item F060; Source: S42-44; T74 objective only

10. For a positive integer m, Γ(m) equals _____.

    Statistics study edition practice item F061; Source: S42-44; T74 objective only

Topic gap report