A famous ubiquitous operating system called Defenestration is run on a lot of computers. For each...

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A famous ubiquitous operating system called Defenestration is run on a lot of computers. For each of the mutually independent computers, the probability mass function for X, the number of operating system crashes in a day, is given by 4-k 10 px (k)= k = 0, 1,2,3. On a day when for a given computer the operating system crashes X = k times, the user has a probability of 1-2-k of reinstalling the operating system. a. Find the mean and variance of X. b. Find the probability that a particular computer has its operating system reinstalled on a given day. c. In a given group of 10 computers, what is the probability that exactly three of them had their operating systems reinstalled on a particular day? A famous ubiquitous operating system called Defenestration is run on a lot of computers. For each of the mutually independent computers, the probability mass function for X, the number of operating system crashes in a day, is given by 4-k 10 px (k)= k = 0, 1,2,3. On a day when for a given computer the operating system crashes X = k times, the user has a probability of 1-2-k of reinstalling the operating system. a. Find the mean and variance of X. b. Find the probability that a particular computer has its operating system reinstalled on a given day. c. In a given group of 10 computers, what is the probability that exactly three of them had their operating systems reinstalled on a particular day?