Question
Asked Nov 14, 2019
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If XXx be Bemoulli random variables, with parameter , then the sufficient
statistic for is
ПХ.
a)
ΣΧ
b)
e
d)
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If XXx be Bemoulli random variables, with parameter , then the sufficient statistic for is ПХ. a) ΣΧ b) e d)

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Expert Answer

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,).

2
Τ(χ') -ΣΧ
sufficient statistics for T
2
Hence for X
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2 Τ(χ') -ΣΧ sufficient statistics for T 2 Hence for X

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Step 2

The sufficient statistics for param...

П
(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
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П (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

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