Clement Cheese Processor, Inc, produces equipment that processes cheese products. Mr. Lambert, the operations manager of this company is particularly concerned about a new cheese processor that has been producing defective cheese crocks. The piece of equipment produces eight (8) cheese crocks during every cycle of equipment. The probability that any one of the cheese crocks is defective is 0.3. Mr. Lambert would like to determine the probability distribution of defective cheese crocks from this new piece of equipment. Based on historical data, the number of defectives produced in a cycle can either be 0, 1, 2, 3, 4, or 5.

a) Find the probability of each of this defect production occurrence in any production cycle of the equipment.

b) Based on your result in question (a), determine the expected value and variance of the probability distribution of this defect production occurrence at Clement Cheese Processor.