Let k be a continuous random variable with the following PDF:

F_K(k) =

{0 for k < 0}

{v * sin(k) for 0 k }

{0 for k > }

1) Determine the numerical value of v

2) Determine the CDF for K, F_K(k)

3) Determine the value that is expected for K, E[K]

4) Determine the probability of K > / 4

5) Denote C being the event that K > / 2. Determine the conditional PDF for K given C, which is f_K|C(k|c).