Unformatted text preview: θ . If the average of a sample of 10 batteries is 36 hours, determine the 95 percent two-sided and both one-sided conﬁdence intervals for θ . The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 4 Suppose X 1 ,...,X n are i.i.d. from normal distribution N ( μ,σ 2 ). Let ¯ X n = ∑ n i =1 X i n (sample mean) and S 2 = ∑ n i =1 ( X i-¯ X n ) 2 n-1 (sample variance). Show that ¯ X n and S 2 are independent random variables. Hint: use the pdf transformation formula of the random vectors and the Jacobian is just some constant. 1...
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- Summer '08
- Normal Distribution, maximum likelihood estimator, One-sided confidence intervals, unknown parameter, one-sided upper confidence