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In March 1995 the Space Shuttle Carried an Experiment Designed p(x)=xexp(x)=x e^{-x}

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In March 1995 the space shuttle carried an experiment designed by a Harvard student who studies the growth of crystals.Suppose the probability density function of the length, x cm, of a crystal grown in space is modeled by p(x)=xexp(x)=x e^{-x} for x0x \geq 0 .The cumulative distribution function giving the probability that a crystal has length \le t cm is represented by P(t).Which of the quantities (i)- (x)below represents precisely the probability that a crystal has length less than 3.01 cm?
 In March 1995 the space shuttle carried an experiment designed by a Harvard student who studies the growth of crystals.Suppose the probability density function of the length, x cm, of a crystal grown in space is modeled by  p(x)=x e^{-x}  for  x \geq 0  .The cumulative distribution function giving the probability that a crystal has length  \le  t cm is represented by P(t).Which of the quantities (i)- (x)below represents precisely the probability that a crystal has length less than 3.01 cm?


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