Question

1. (Discrete R.V. and Probability Mass Function) Suppose you work at a banana factory, where there is a conveyor belt along which bananas are always coming your way. Each banana is rotten w.p. 0.3, independent of all else. The first time that you get a rotten banana, you have to shut down the plant operations for the day. Until that time, you process the fresh bananas you receive as follows.

   • The first 90 fresh bananas you process must be packed into crate 1.

   • The next 80 fresh bananas you process are given to charity.

   • If you continue to see fresh bananas, the next 100 fresh bananas you process must be packed into crate 2.

   • All remaining fresh bananas are given to charity.
     N2 be the total number of bananas you put in crate 2, and B be the total number of bananas you give

     to charity.

     1. (a) Express N2 as a function of appropriate r.v.

     2. (b) Write the p.m.f. of N2, i.e. list all possible values that N2 can take and for each value x, give the expression for P (N2 = x).

     3. (c) Express B as a function of appropriate r.v.

     4. (d) Write the p.m.f. of B, i.e. list all possible values that B can take and for each value x, give the

        expression for P (B = x).

Answer 1

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