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What is the probability that it snows 2 times in a 10 day

1. The probability that it snows on any day in Toronto, ON is 0.25. For the purposes of this question, assume that snowfall (or the absence of snowfall) does not affect the probability of snow happening on any other day.

(a) What is the probability that it snows 2 times in a 10 day period?

(b) In a 7 day period, what is the probability that it snows at least 5 times?

2. A French major is about to graduate and enter the job market. Her wage earnings (w) in the first year after graduating are distributed as follows. With probability 0.70, she will receive a random draw of w from a normal distribution with a mean of 60,000 and a variance of 5,000. With probability 0.30, she will instead receive arandom draw of w from a normal distribution with a mean of 70,000 and a variance of30,000.

(a) Write down the formula for the CDF of w.

3. Suppose that unlike the student in the previous question (#3), you have the choice between receiving a salary drawn from a N(µ = 60, 000, σ2 = 5, 000) distribution, or instead receiving a salary drawn from a N(µ = 70, 000, σ2 = 30, 000) distribution. Which distribution would you prefer to draw from? Why? Justify your answer using reasoning based on both statistics and economics.

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