Question: Many named distributions are special cases of the more common distributions already discussed. For each of the following named distributions derive the form of the pdf, verify that it is a pdf, and calculate the mean and variance.
- IfX~exponential(β), then
has the Weibull (γ,β) distribution, where
is constant.
(c)If X~gamma(a, b),then
has the inverted gamma IG(a, b) distribution.
(This distribution is useful in Bayesian estimation of variances; see Exercise7.23 below)
Deliverable: Word Document 
![[Step-by-Step] Let and be independent n(0, 1)](/images/solutions/MC-solution-library-64141.jpg "[Step-by-Step] Let and be independent n(0, 1) random variables. Find")
[Step-by-Step] Let and be independent n(0, 1) random variables. Find
![[Step-by-Step] Let and let . Suppose X](/images/solutions/MC-solution-library-64142.jpg "[Step-by-Step] Let and let . Suppose X and Y are independent.")
[Step-by-Step] Let and let . Suppose X and Y are independent.
![[Step-by-Step] Show that if follows a binomial](/images/solutions/MC-solution-library-64143.jpg "[Step-by-Step] Show that if follows a binomial distribution with")
[Step-by-Step] Show that if follows a binomial distribution with
(Solution Library) Identifying H 0 and H 1 - In Exercises 1 2,
![[See Solution] The world’s smallest mammal is](/images/solutions/MC-solution-library-64145.jpg "[See Solution] The world’s smallest mammal is the bumblebee bat,")
[See Solution] The world’s smallest mammal is the bumblebee bat,
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