L [NJ In studying the behavior of air support roofs. the random variables X. the inside barometric pressure (in inches of mercury) and Y, the outside barometric pressure are considered. Assume that the joint density is given by 1 _v. IEyEEI. 0:51:12 fn'lx-J') = 4 III}. eismvherc (i) Find ELK], E[XY]. (ii) Are X. Y independent? Explain. ' Rockwell hardness of pins of a certain type is known to have a mean value of SID and a standard deviation of 1.2. a) If the distribution is normal. what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51? b} What is the {approximate} probability that the sample mean hardness for a random sample of 412) pins is at least 51? U