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Chi - square. Distributions of functions of r.v.s. X – has a probability density function f(x) We define Y = g(X), where g(.) is monotonic function What is the distribution of Y ?. Examples. 2 with 1 degree of freedom (d.f.). What is the distribution of Y ?.

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## Chi - square

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**Distributions of functions of r.v.s**X – has a probability density function f(x) We define Y = g(X), where g(.) is monotonic function What is the distribution of Y ?**2 with 1 degree of freedom (d.f.)**What is the distribution of Y ?**f(x)**x f(v) v**f(y)**y**2(n d.f.)**2(n d.f.) = 2(1 d.f.)* 2(1 d.f.) …* 2(1 d.f.) n times**2 and multinomial distribution**Multinomial distribution – K possible outcomes of an experiment probabilities: p1, p2, …, pK, p1+p2+ …+pK=1 N - experiments**For large N**Becomes 2(K-1 d.f.)

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