(Solved): 4a) The cumulative distribution function, \( F(x) \), of a continuous random variable \( x \) is a ...

4a) The cumulative distribution function, \( F(x) \), of a continuous random variable \( x \) is as follows: \( F(x)=1-\exp (-2 x) \) for \( x>0 \). (i) \( P(X>1 / 2) \) (ii) \( P(X=5) \) (iii) What is the probability density function of \( X \) ?