我有一個大學的機率數學題 ><!急
check whether x and y are independent if their joint probability distribution is given by
(a) f(x,y)=1/4 for x= -1 and y= -1, x= -1 and y=1, x=1 and y= -1, and x=1 and y=1
(b)f(x,y)=1/3 for x=0 and y=0 , x=0 and y=1 , and y=1 , and x=1 and y=1
please steps by steps
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Verified answer
a、 f(x,y)：f(0,0)=f(0,1)=f(1,0)=f(1,1)=1/4f(x=0)=1/4+1/4=1/2f(x=1)=1/4+1/4=1/2f(y=0)=1/4+1/4=1/2f(y=1)=1/4+1/4=1/2for all x=0 ,1 and y=0, 1f(x,y)=f(x)*f(y)x and y are independent b、f(x,y)：f(0,0)=f(0,1) =f(1,1)=1/3f(x=0)=1/3+1/3=2/3f(x=1)=1/3f(y=0)=1/3f(y=1)=1/3+1/3=2/3f(0,0)=1/3≠f(x=0)*f(y=0)=2/3*1/3=2/9x and y are dependent