Kindly help me solve these problems clearly showing step by step

A firm has technology represented by the following production function: f ( L, K) = L^1/3 K ^2/3 It would like to produce 122 units. It operates in competitive input markets where the price of labor is $6 and the price of capital is $9. What amount of labor does the firm use when it is producing its desired level of output in the least costly way?5-57. Suppose that X has a standard normal distribution. Let the conditional distribution of Y given X = x be normally dis- tributed with mean E(Y | x) = 2x and variance V(Y | x ) = 2x. Determine the following. (a) Are X and Y independent? (b) P(Y