Q1. A random variable X has the following probability density function. 1 for 0 S x

QI. A random variable X has the following probability density function. 1 forOsx < 0.5 f(x)= -x + c for 0.5 s x < 1.5 elsewhere a) b) c) d) Show thatc = 1.5 Find the mean of X. Determine the probability P(O < X 1). Determine the cumulative distribution function of X.