Practice_problems_2.pdf - [1(9 marks The breakdown voltage...

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A-2 [1] (9 marks) The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with mean value 40 V and standard deviation 1.5 V. (a) What is the probability that the voltage of a single diode is between 39 and 42? (b) What value is such that only 20% of all diodes have voltage exceeding that value? (c) If four diodes are independently selected, what is the probability that at least one has a voltage between 39 and 42?
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A-3 [2] (6 marks) Using a long rod that has length ° , you are going to lay out a square plot in which the length of each side is ° . Thus the area of the plot will be ° . However you do not know the value of ° , so you decide to make ! independent measurements " # , " , . . . , " % of the length. Assume that each " & has mean ° (unbiased measurements) and variance . (a) Show that " ( is not an unbiased estimator for ° . (b) For what value of ) is the estimator " ( − )+ unbiased for ° . (hint: + is an unbiased estimator of )
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A-4 [3] (8 marks) Circle the best answer. (i) Suppose a 95% confidence interval for ° turns out to be (1000, 2100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of
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