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\fa) Suppose that a population only has one number, 50. What is its variance? b) Suppose that the mean of a sample with 10 observations is 11. Now a new observation is added to the sample. If the value of the new-added number is ll, will the mean of the new sample still be 11? Why or why not? c) Suppose that the mean and variance of a sample with 10 observations are 11 and 30, respectively. Now, a new observation is added to the sample. If the value of the 11th number is 11. What is the variance of the new sample? (1) Note that variance = (standard deviation) * (standard deviation) and that the standard deviation cannot be negative. For example, if the variance is 9, then the standard deviation is 3, not 3. Is it possible to have a sample with 10 integer numbers whose variance is smaller than its standard deviation? If yes, provide an example. If not, provide a short reason. Suppose that, to battle against COVlD-l9, Health Canada has approved two laboratory tests that identify SARS-CoV-Z, the virus that causes COVlD- 19. When a person, who either contracts COVID l9 virus (C = Contracted) or not (C C = Not Contracted), arrives at a test location, the rst test will be applied on him/her and will mark him/her as positive (+) or negative () for SARSCoV-2. If the result is positive, the second test program will be applied on him/her later on to see if he/she has contracted or not contracted COVIDl9. Assume that 10% of all tested carry the SARS-CoV-2 virus and that the two tests are each \"90% accurate\" in the sense that P (+]C ) = P(| C C) = 0.9 for each test. Also assume that given whether a person carries the SARS-CoV-Z virus, the two tests' outputs are conditionally independent. a) Find the probability that the person carries the virus, given that the rst test marks him/her as positive. b) Find the probability that the person carries the virus, given that both tests mark him/her as positive