The following outcomes were from a random sample of size 25 from the joint distribution of \((Y, X)\), where \(Y\) denotes yield, in bushels per acre, of a new variety of overlineley and \(X\) denotes average inches of rainfall during the growing season:

(a) Define the joint EDF for the underlying joint CDF of yield and rainfall.

(b) Define the marginal EDF for the underlying CDF of yield.

(c) Define the sample covariance and sample correlation between yield and rainfall based on the EDF you defined in (a).

(d) Treating the EDF as the true CDF of \((Y, X)\), estimate the probability that yield will be greater than 75 bushels per acres.

(e) Use the EDF to estimate the probability that yield will be greater than 75 bushels per acre, given that rainfall will be less than 20 inches.

(f) Use the EDF to estimate the expected yield.
(g) Use the EDF to estimate the expected yield, given that rainfall will be less than 20 inches.

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Y X 81.828 26.195 17.102 71.305 75.232 21.629 75.936 17.553 74.377 24.760 Y 77.903 17.091 79.645 17.867 72.966 19.094 74.051 21.304 24.847 78.050 77.149 22.788 74.878 23.053 81.959 25.566 68.752 13.607 75.094 19.819 71.925 21.738 76.299 81.166 21.407 77.723 19.190 83.792 72.750 18.410 73.022 75.413 26.478 78.167 73.079 19.744 21.829 35.889 23.079 21.155