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For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?

  1. $a=1,b=4$
  2. $b=0.5,b=1$
  3. $a=0,b=1$
  4. $a=1,b=-1$
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