# If XXx be Bemoulli random variables, with parameter , then the sufficientstatistic for isПХ.a)ΣΧb)ed)

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39 views help_outlineImage TranscriptioncloseIf XXx be Bemoulli random variables, with parameter , then the sufficient statistic for is ПХ. a) ΣΧ b) e d) fullscreen
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Step 1

Bernoulli distribution:

Bernoulli distribution is a discrete probability distribution in which the experiment tend to have only two possible outcomes. In addition, it will have single trial of experiment. The probability of success in Bernoulli distribution is denoted by p and the probability of failure is denoted by q.

For a X1, X2… Xn random variable follows a Bernoulli distribution with parameter . Therefore the sufficient statistics for is, here T(Xn) has binomial (n,).

Step 2

The sufficient statistics for param... help_outlineImage TranscriptioncloseП (1-7) f(x") i1 (T(x)) (1 -r) п |т (1—т)"* t п(1—т) (3ra-2)" |т"(1—л)" 1 = n 1 Σ. i=1 fullscreen

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