The length of time it takes a baseball player to swing a bat (in seconds) is a continuous random variable X with probability density function (p.d.f)

f(x) = ax+ 8/9 for 0<= x <= b and f(x) = 0 otherwise.

a) determine the unique values of a and b necessary to ensure that the function f(x) is a valid p.d.f with mean equal to 2/3.

b) calculate the median of X

Thanks!