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The 2020 death rate of COVID patients that reside in New York nursing homes was 14%. The population of New York nursing home residents is very large in the hundreds of thousands.
Suppose we take a random sample of 9 nursing home residents on Jan 1, 2020, and suppose we observe a random variable X = of number of COVID deaths out of the 9 residents by Jan 1, 2021.
a. What is the distribution of X? Please justify your answer.
b. Calculate the probability that X is greater than zero.
c. Give the probability of only one death and the probability that all 9 are dead.
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