Suppose the chance of rain in Chicago and Minneapolis are correlated. Define X = 1 if it is raining in Chicago some day and X = 0 if not; Similarly, define Y = 1 if it is raining in Minneapolis and Y = 0 otherwise. Now we know the probability of raining in Chicago and Minneapolis are both 0.35, i.e., P(X = 1) = 0.35 and P[Y = 1) = 0.35. Now (a) If given it rains in Chicago, the probability of rain in Minneapolis is 0.7. What is the correlation between X and Y? (b) If we know the correlation between X and Y is 0.5, what is the conditional probability that it rains in Minneapolis rains given it rains in Chicago?

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a To find the correlation between X and Y we can use the formula for correlation XYEX... View the full answer