Let X11 X12X1, and X2₂1, X22, X2na be two independent random samples ofsize ni and n₂ from two normal populations N(₁, of) and N(2, 2) respectively.(d) Derive a (1-a) x 100% confidence interval for (₁-2) when both samples aresmall but of and o are known.(e) Discuss how the confidence interval in part (c) will change if both the samples arelarge.

Given that samples are random and independent. The size of the samples is small and the population…

Answered: Let X₁1X12X1, and X21, X22X2, be two…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.
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A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…
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Let X₁1X12X1, and X21, X22X2, be two independent random samples of size ny and n₂ from two normal populations N(₁, of) and N(2, 2) respectively. (d) Derive a (1-a) x 100% confidence interval for (μ₁ −µ₂) when both samples are small but of and of are known.