Let x denote the amount of time a book on 2-hour reserve in the library is checked out by a randomly selected student. Suppose x has the density functionf(x)=0.5x for 0≤x≤2 otherwise f(x)=0Compute the following probabilities. Give answers to two decimal places. a. P(x≤1.6)b. P(0.8≤x≤1.6)c. P(x>1.2)d Find the median time the book is checked out. e Find the mean time the book is checked out. probability density function:The probability density function can be used to obtain the probability of a random variable by integrating within the limits. The function should be positive and the area under the curve should be equal to 1.