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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2009-10) EXAMPLE CLASS 3 1. A coin has a probability p to turn up a head when tossed. It was tossed 100 times and 55 heads turned up. Write down the likelihood function. 2. Assume the height of a student is normally distributed with mean μ and variance σ 2 , the heights of 5 randomly selected students were measured to be 1.76, 1.68, 1.82, 1.75 and 1.78. Write down the likelihood function. 3. A sample of size 10 is drawn at random without replacement from a population of size N = 1000, in which there are m males and N- m females and m is not known. It is found that there are two males in the selected sample. Write down the likelihood function. 4. An archer shoots arrows repeatedly at a target until he gets exactly 3 hits. It may be assumed that the probability for an arrow to hit the target is p , and the shots are independent of one another....
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