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.

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?