If a random variable X has the gammadistribution with a = 2 and B = 1, find P(1.8

Answered: If a random variable X has the gamma…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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 x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.3%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.3%? Use α = 0.01. (a) What is the level of significance? (Enter a number.)State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ > 4.3%; H1: μ = 4.3%; right-tailedH0: μ = 4.3%; H1: μ ≠ 4.3%; two-tailed H0: μ = 4.3%; H1: μ < 4.3%; left-tailedH0: μ = 4.3%; H1: μ > 4.3%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal…
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Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.4%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: H = 4.8%; H1: µ ± 4.8%; two-tailed Ho: H = 4.8%; H1: µ > 4.8%; right-tailed Ho: H = 4.8%; H1: µ 4.8%; H1: µ = 4.8%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown o. The Student's t, since we assume that x has a normal distribution with known o. The standard normal, since…
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If a random variable X has the gamma distribution with a = 2 and B = 1, find P(1.8