Question: Suppose that the random variable X has cumulative distribution function F(x)= F(x)={0ifx <2^(1/2),x^22 if2^(1/2)x <3^(1/2), 1 ifx3^(1/2) Find the smallest interval[a,b] such that P(aXb)=1.a =b

Suppose that the random variableXhas cumulative distribution functionF(x)=

F(x)={0ifx<2^(1/2),x^22 if2^(1/2)x<3^(1/2), 1 ifx3^(1/2)

  1. Find the smallest interval[a,b] such that P(aXb)=1.a =b =
  2. P(X=1.6).Prob =
  3. FindP(1X8/5)=
  4. Find the probability density function ofX. Give an equation for it on the interval you found in part (a). (Outside of this interval, the density is 0.)f(x)

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