Problem 3 [16 points (4 pts each)]: Poisson Distribution Let's estimate the average rate at which companies have large data breaches to be once every ten years. (We'll simply refer to this as \"being hacked\" henceforth.) We'll further assume that the distribution on the number of large breaches is Poisson; being hacked once is no protection against further hacks. i Calculate the likelihood that a company is hacked exactly once in a particular year. (Hint: The expected number of hacks is a fractiOn.) You can round to two decimal places. ii Calculate the likelihood that a company is not hacked at all in a particular year. (Note that O! = 1.) Again, you can round to two decimal places. iii Using your previous results, calculate the likelihood that a company is hacked two or more times in a particular year. (Hint: A company must fall in this category if it doesn't fall in the rst two.) iv Given that there are 5.6 million companies in the United States, use linearity of expectation to nd the expected number of US. companies hacked at least twice in a year. You can estimate to the nearest thousand, using your previous calculatiOns