(Solved): A random variable has the following distribution. i- Find the constant \( c \). ii- Find cumulative ...

A random variable has the following distribution. i- Find the constant \( c \). ii- Find cumulative distribution function (CDF). iii- Find \( E(x), E\left(x^{2}\right) \) and \( E\left(1-2 x^{2}\right) \). iv. Find the variance \( \operatorname{var}\left(\frac{x}{2}\right) \) and standard deviation \( \sigma_{x} \).