Nonl P(D = k) =)m theta k) ((1 - theta)m n - k) (m n)^-1, max{n - m(1 - theta),

Question

Nonl P(D = k) =)m theta k) ((1 - theta)m n - k) (m n)^-1, max{n - m(1 - theta), 0} lessthanorequalto k lessthanorequalto min{m theta, n}. Is the above a hypergeometric probability distribution H(m theta, m, n)? One-sample model: For X_1, ..., X_n i.i.d. from the population X ~ P P, each specification of the family P defines one model. For example, Measure model: the observation X_i = mu + epsilon_i, with i.i.d. random error epsilon_i's. Location model: the random error sigma_i ~ G and hence X_i ~ F(x) = G(x - mu). Gaussian model: i.i.d. random errors and epsilon_i ~ N(0, sigma^2) and hence X_i ~ N(mu, sigma^2). So, as one specification Gaussian model assumes P = {phi(x - mu/sigma): mu R, sigma^2 > 0}, phi(x) = integral_-infinity^x e^-y^2/2 dy. Is the above a normal probability distribution?

Explanation / Answer

1) Yes, given function is related to Hypergeomentric distribution, since given function, Limits about parameters are exactly equal to properties of hypergeomentric distribution.

2) No, Given properties are not fullfil of normal distribution, since pdf should contain a constand term 1 / sqrt(2)

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