(Step-by-Step) [10pts] The joint probability density function for the random variables Y 1 and Y 2 is given by f(y_1,y_2)=4y_1y_2 0≤ y_1≤ 1, 0≤ y_2≤
Question: [10pts]
The joint probability density function for the random variables Y 1 and Y 2 is given by
\[\begin{aligned} & f({{y}_{1}},{{y}_{2}})=4{{y}_{1}}{{y}_{2}}\text{ 0}\le {{\text{y}}_{\text{1}}}\le 1,\text{ 0}\le {{\text{y}}_{\text{2}}}\le 1 \\ & \text{ 0, elsewhere}\text{. } \\ \end{aligned}\]
Show that Cov(Y 1 , Y 2 ) = 0.
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