The density function of a Gamma with parameters α and λ is (a) Find its moment generating function (m.g.f.). (c) Use the
Posted: Sat Feb 26, 2022 11:00 am
The density function of a Gamma with parameters α and
λ is
(a) Find its moment generating function (m.g.f.).
(c) Use the central limit theorem to approximate a Gamma(n,
λ) as n → ∞.
1° /T(a)x9-1 exp(- 4x).
2 Let X1, ..., Xn be an i.i.d. sample from an exponential density Exp(\). Show that i= X; ~ Gamma(n, 1) and that 21 - X; 1 Xản i=1
2 2nXGamma(n, 1) has a Xîn distribution. Using this, find the m.g.f. and mean and variance of a xa random variable.
λ is
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λ) as n → ∞.
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2 Let X1, ..., Xn be an i.i.d. sample from an exponential density Exp(\). Show that i= X; ~ Gamma(n, 1) and that 21 - X; 1 Xản i=1
2 2nXGamma(n, 1) has a Xîn distribution. Using this, find the m.g.f. and mean and variance of a xa random variable.