Unformatted text preview: 525 hours? 3. A die is continually rolled until the total sum of all rolls exceeds 300. What is the probability that at least 80 rolls are necessary? 4. Let ? 1 , ? 2 , … , ? ± be a random sample of size ± from the exponential distribution whose pdf is given by ´ ( µ ) = ¶· −¶µ , µ > 0, ¶ > 0 a) Show that the sample mean ? is an unbiased estimator of 1 ¶ . b) Given a random sample of size 5 : 3.5, 8.1, 0.9, 4.4, 0.5 , find a point estimate of ¶ . 5. Let ? ¸ , ¸ = 1,2, … , ± be Bernoulli random variables such that ? ¸ = ¹ 1 , º , 1 − º a) Show that ? is an unbiased estimator of º . b) Find an unbiased estimator of the variance of ? ....
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 Fall '10
 MrChung
 Statistics, Probability, Standard Deviation, Variance, Probability theory, unbiased estimator, STATISTICS AND ACTUARIAL SCIENCE

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