Question

Common discrete distributions include • Uniform(0,n), p(x) = \frac{1}{n}, x = 0,1,..., n, • Poisson(?), p(x) = \frac{?^x e^{-?}}{x!}, x = 0, 1, ..., ?, • Bernoulli(p), p^x(1 - p)^{1-x}, x = 0, 1, • Binomial(n, p), p(x) = \binom{n}{x}p^x(1 - p)^{n-x}, x = 0, 1, ..., n, • Geometric(p), p(x) = p(1 - p)^x, x = 0,1,...,?, • Negative Binomial(m,p), p(x) = \binom{m+x-1}{m}p^m(1-p)^x, x = 0,1,..., ?, Please find the moment generating function of these distribution laws. Use it to calculate the first 4 moments, then calculate the variance and skewness.

          Common discrete distributions include
• Uniform(0,n), p(x) = \frac{1}{n}, x = 0,1,..., n,
• Poisson(?), p(x) = \frac{?^x e^{-?}}{x!}, x = 0, 1, ..., ?,
• Bernoulli(p), p^x(1 - p)^{1-x}, x = 0, 1,
• Binomial(n, p), p(x) = \binom{n}{x}p^x(1 - p)^{n-x}, x = 0, 1, ..., n,
• Geometric(p), p(x) = p(1 - p)^x, x = 0,1,...,?,
• Negative Binomial(m,p), p(x) = \binom{m+x-1}{m}p^m(1-p)^x, x = 0,1,..., ?,
Please find the moment generating function of these distribution laws. Use it to calculate the first 4 moments,
then calculate the variance and skewness.

Common discrete distributions include
• Uniform(0,n), p(x) = (1)/(n), x = 0,1,..., n,
• Poisson(?), p(x) = (?^x e^-?)/(x!), x = 0, 1, ..., ?,
• Bernoulli(p), p^x(1 - p)^1-x, x = 0, 1,
• Binomial(n, p), p(x) = nxp^x(1 - p)^n-x, x = 0, 1, ..., n,
• Geometric(p), p(x) = p(1 - p)^x, x = 0,1,...,?,
• Negative Binomial(m,p), p(x) = m+x-1mp^m(1-p)^x, x = 0,1,..., ?,
Please find the moment generating function of these distribution laws. Use it to calculate the first 4 moments,
then calculate the variance and skewness.

Added by Zachary S.

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