Let X1,X2,... be a sequence of independent uniform (0, 1) random variables. For a fixed co...

Let X1,X2,... be a sequence of independent uniform (0, 1) random variables. For a fixed constant c, define the random variable N by

N = min{n : Xn > c}

Is N independent of XN? That is, does knowing the value of the first random variable that is greater than c affect the probability distribution of when this random variable occurs? Give an intuitive explanation for your answer.