Homework100B7

# Homework100B7 - x i are ﬁxed and ± i ∼ N(0,σ 2...

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STAT 100B HW 7 Due Friday Problem 1: Suppose X 1 ,X 2 ,...,X n Bernoulli( p ) independently. Please calculate the maximum likelihood estimate of p . Problem 2: Suppose X 1 ,X 2 ,...,X n N( μ,σ 2 ) independently. Please calculate the maximum likelihood estimate of ( μ,σ 2 ). Problem 3: Suppose X 1 ,X 2 ,...,X n Exponential( λ ) independently. Please calculate the maxi- mum likelihood estimate of λ . Problem 4: Suppose y i = x i β + ± i , for i = 1 ,...,n , where
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Unformatted text preview: x i are ﬁxed, and ± i ∼ N(0 ,σ 2 ) indepen-dently. Find the maximum likelihood estimate of ( β,σ 2 ). Problem 5: Suppose y i ∼ Bernoulli( p i ) independently, for i = 1 ,...,n , and log[ p i / (1-p i )] = x i β , where x i are ﬁxed. Write down the log-likelihood function of β , and calculate the derivative of the log-likelihood function. 1...
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