For a random variable X, Does there exist a value x and a random variable X, suc

Question

For a random variable X, Does there exist a value x and a random variable X, such that CDF F_x(x) > 1. If yes, give an example; if not, prove it. Does there exist a value x and a random variable X, such that PDF f_x(x) > 1. If yes, give an example; if not, prove it. Prove that E(X^2) greaterthanorequalto [E(X)]^2, and show when "="is achieved. Let X be a non-negative random variable with CDF F, prove that E(X) = integral_0^infinity P(X > x) dx and E(X^n) = integral_0^infinity nx^n - 1 P(X > x) dx, where n is a positive integer.

Explanation / Answer

the cdf given above is true because the value of x exists and random variable of xi s true if probability function is greater than equal to 1then it is one if not it is zero

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