7. Assume that the number of shares of a stock market in the UK bought over time follows a Poisson distribution with a rate à = 12 per minute. 1) How many minutes will it take for 36 shares to be bought with a probability of at least 94.8%? Denote by n this minimum number of minutes. 2) Calculate the average waiting time for 40 shares to be purchased. 3) Let's assume that same stock is also sold on a stock market in the US. We assume that, on the US market, the number of its shares bought in time also follows a Poisson process but with a rate of u = 8 per minute. Calculate the probability that the total number of shares (bought in the two markets combined) in n minutes is greater than 72.

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