HGh-IEWDRK 3 STAT 414 Fall 2022 1. (3D points} A tank has Lll fish, and 2f] of them are orange while the rest have a different color. {a} Suppose that 1l'l fish are extracted from the tank at random without replacement. Let Y be the random Iu'ariable that counts the number of orange fish in the sample. What is the distribution of 1'? What is the probability.r that the sample contains two orange fish or less? Use the prnf. {b} hlo'llirr suppose that one fish at a time is extracted from the tank at random and returned to the tank afterwards before extracting the next fish. This process is repeated until extracting two orange fish. Let X be the number extractions performed. What is the distribution of X? 1I.I"'.|'hat is the probability.r that 1D or less extractions were performed to observe 2 orange fish? Use the prnf. {c} If 10 fish are extracted with replacement [as in [bl] and Z is the number of orange fish observed in these 10 extractions. what is the distribution of 2'? 1I.I"'.|'hat is the |::uro|:nabilit.uI that Z i: 2? Use the prnf