(Solved): Consider the joint probability distribution below. Complete parts (a) through (c). a. Compute the ...

Consider the joint probability distribution below. Complete parts (a) through (c). a. Compute the marginal probability distributions for \( \mathrm{X} \) and \( \mathrm{Y} \). (Type integers or decimals.) b. Compute the covariance and correlation for \( \mathrm{X} \) and \( \mathrm{Y} \). \( \operatorname{Cov}(X, Y)=\quad \) (Round to four decimal places as needed.) \( \operatorname{Corr}(\mathrm{X}, \mathrm{Y})=\quad( \) Round to three decimal places as needed. \( ) \) c. Compute the mean and variance for the linear function \( W=X+Y \). \( \mu_{\mathrm{W}}=\quad \) (Round to two decimal places as needed.) \( \sigma_{W}^{2}= \) (Round to four decimal places as needed.)