"P(X=0)="
"P(X=0,Y=0)+P(X=0,Y=1)="
"0.3+0.2=0.5",
"E(X)=0.5\\cdot0+0.5\\cdot1=0.5",
"P(Y=0)="
"P(X=0,Y=0)+P(X=1,Y=0)="
"0.3+0.2=0.5",
"E(Y)=0.5\\cdot0+0.5\\cdot1=0.5",
"cov(X,Y)="
"0.3(0-0.5)(0-0.5)+"
"0.2(0-0.5)(1-0.5)+"
"0.2(1-0.5)(0-0.5)+"
"(1-0.3-0.2-02)(1-0.5)(1-0.5)="
"0.3(-0.5)(-0.5)+0.2(-0.5)0.5+"
"0.2\\cdot0.5(-0.5)+0.3\\cdot0.5\\cdot0.5=0.05>0,\\implies"
"corr(X,Y)>0",
Therefore X and Y are are positively correlated.
For independent variables correlation is equal 0,but "corr(X,Y)>0",
therefore X and Y are dependent.
Answer: (d). X and Y are positively correlated and dependent.
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