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Statistics

Let {X1, X2,...XN} be a random sample where each random variable X, has a PDF given by

f(x)=\frac{1}{(\lambda+\mu)} e^{\frac{1}{2}[-(\operatorname{sign}(x)+1)(x / \lambda)+(\operatorname{sign}(x)-1)(x / \mu)]}

\operatorname{sign}(x)=\left\{\begin{array}{rr} 1, & x \geq 0 \\ -1, & x<0 \end{array}\right.

where the sign function is defined as

and N denoting an integer, and the parameters , µ satisfying 1 > 0, µ > 0.In the followings provide complete derivations and explanations of results.

a) Find the likelihood function and the log-likelihood function for the parameters 1,µ

b) Find Maximum Likelihood (ML) estimators for the parameters 1, u.

c) Determine if these ML estimators are unbiased for N = 1.

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Statistics

How many ways can 4 pairs of socks be chosen from 16 pairs?

O 1820

O 496

O43680

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Statistics

How many subsets of {1,2,.... 20} have three elements?

O 5814

01140

O 969

O 6840

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Statistics

Suppose there are eight different colors of flowers in a flower vase. How many different ways we select three different colors of flowers from the vase?

0 6720

O 336

06

56O 56

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Statistics

How many eight-digit integers are there that do not contain repeated digits?

O 10-9 8 7-6 5-4-3

09.9.8-7-6 5 4-3

O P(10, 8)

O P(9, 8)

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Statistics

How many 2-permutations of {a, b, c, d)?

O 12

O 24

O 10

O 35

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Statistics

How many permutations of the letters ABCDEFG contain the string "BC" and "FG'as a substrings?

O 120

0720

O 2520

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Statistics

How many permutations of the letters ABCDEFG contain the string "ABC as a substring?

O 5040

0 120

O 24

0720

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Statistics

How many different order can there a set with {a, b. c. 4. 5. Š}?

O 120

O 1040

0720

O 24

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Statistics

How many numbers from the set of integers between 1 and 1000, inclusive, are divisible by 2 or 5.

O 600

O 500

O 300

0400

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