I only need help with 16 and 17!

Ana is an entrepreneur in a developing country who produces ponchos in a sewing room in her home. (She is part of the \"informal\" manufacturing sector.) The number of ponchos Ana produces per day is a random variable X, which has the probability distribution given below. Numbers of ponchos produced on different days are independent. x 39 40 41 42 Px(x) 0.3 0.4 0.2 0.1 6. Calculate the probability Ana will produce more than 40 ponchos on any one day. One decimal 7. Calculate the expected number of ponchos Ana produces in a day. One decimal 8. Calculate the variance of the number of ponchos produced in a day. Two decimals 9. Calculate the probability that, in a period of five days, Ana will produce more than 40 ponchos on at least one day. HINT: You can answer this question, and the next one, using the binomial probability function, but that is not necessary. Four decimals 10. Calculate the probability that Ana will produce more than 40 ponchos on all ve days. Four decimals 11. The production cost of a poncho (in dollars) is Y = 2 + 24(1/X). Calculate expected cost per poncho. Four decimals HINT: Begin by specifying the probability distribution of Y (the different possible values of Y, and the probability that each will occur). Alternatively, you can specify the probability distribution of 1/X, and then use the results we have about the mean and (in the next question) variance of a linear transformation. (Y is n_ot a linear transformation of X, but Y i_s a linear transformation of 1/X.) 12. Calculate the variance of cost per poncho. HINT: Keep more than 4 decimals when you do the calculation, because the answer is a small number. Four decimals 13. Revenue per poncho (in dollars) is R = 12 0.1x. (This revenue function reflects the fact that Ana must cut the price in order to sell more.) Calculate expected revenue per poncho. HINT: Use our results about the mean and (in the next question) variance of a linear transformation. Two decimals 14. 15. 16. 17. 18. Calculate the variance of revenue per poncho. Four decimals Prot per poncho, Z, is revenue per poncho minus production cost per poncho (Z = R Y). Calculate expected profit per poncho. HINT: Use our result about the mean of a linear combination. Four decimals Calculate the covariance between the number of ponchos (X) and cost per poncho (Y). Four decimals HINT: You must write down the joint distribution of X and Y to obtain the covariance. This is not hard! It is a 4x4 joint distribution. There are 4 rows (one for each value of Y) and 4 columns (one for each value of X). However, only the \"diagonal" pairs of values occur with positive probability. This means there will be only four terms in the covariance. Calculate the covariance between revenue per poncho (R) and cost per poncho (Y). Five decimals HINT: You can calculate this second covariance from the covariance between X and Y, using our result about the effect of linear transformations on the covariance. Calculate the variance of prot per poncho. Four decimals HINT: Use our result about the variance of a linear combination