PDF of Gamma (Γ) Distribution for α = 9, k = 3 & x = 11
Gamma (Γ) distribution example problem workout with steps & calculation summary for the probabilty density function (PDF) of the random variable x = 11, scale parameter k = 3 and shape parameter α = 9 in statistical experiments.
| Calculation Summary | |
|---|---|
| Shape Parameter (α) | 9 |
| Scale Parameter (k) | 3 |
| random variable (x) | 11 |
| 0.0069 | |
| mean (µ) | 27 |
work with steps for α = 9, k = 3 & x = 11
Question:
A gamma distribution which has the shape parameter α = 9 and scale parameter k = 3. Find the probability density function P(x) for the random variable x = 11?
workout :A gamma distribution which has the shape parameter α = 9 and scale parameter k = 3. Find the probability density function P(x) for the random variable x = 11?
step 1 Addres the formula input parameter and values
shape parameter α = 9
scale parameter k = 3
x = 11
step 2 Find probability density function using k, α & x values
PDF = (x)(α - 1) e -(x/k)Γ(α) kα
= (11)(9 - 1) e -(11/3)Γ(9) 39
= (11)(8) e -(3.6667)Γ(9) (3)9
40320 is the gamma value of 9
= (214358881) (0.0256)(40320) (19683)
= 5479341.6548/793618560
PDF = 0.0069
step 3 Find Mean value using shape & scale parameter
Mean µ = k x α
= 3 x 9
Mean µ = 27
