3. A individual visits a large mango orchard with very large number of very large trees, where the probability of picking a ripe mango is p and is independent of other picked mangoes. The individual decides to pick ripe mangoes from single tree until an unripe mango is picked. If an unripe mango is picked, the individual changes trees. a. Let Ma the number of mangoes picked from the ith tree. What is the PMF, expectation value, and variance of Ma. b. Let Xi be the total number of ripe mangoes picked from i trees. What is the expected value and variance of X3.
c. What is the joint PMF of XI and X2? d. Are M3 and X2 independent? Why?