f (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is a pdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphs of the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.

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A: Hey there! Thank you for posting the question.  Since you have posted a question with multiple…

Q: Let x represent the average annual salary of college and university professors (in thousands of…

A: The null and the alternative hypotheses are, H0: σ2≤47.1 HA: σ2&gt;47.1 Test statistic: Thus, the…

Q: Let x represent the average annual salary of college and university professors (in thousands of…

A: Given information- Sample size, n = 19 Sample variance, s2 = 79.8 Confidence level, c = 95% a)…

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Q: Let x represent the average annual salary of college and university professors (in thousands of…

A: (a)The correct null and alternative hypothesis is as follows:   H0: σ2 = 47.1   H1: σ2 &gt; 47.1 (b)…

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Q: Let x represent the average annual salary of college and university professors (in thousands of…

A: Given information- Sample size, n = 19 Sample variance, s2 = 80.5 Confidence level, c = 95%…

Q: Let x represent the average annual salary of college and university professors (in thousands of…

A: From the provided information, The hypotheses can be constructed as: Null hypothesis: H0: σ2 = 47.1…