Probability Question

Question

Spongebob is going Jellyfishing (that is, he seeks to capture jellyfish in a net, and then release them, of course).

He plans to try his luck in two separate fields. Note that he is going to go to both fields, and the outcomes in each field are independent of each other.

1. The first field has jellyfish with probability 0.60, while the second has jellyfish with probability 0.75 (these probabilities are independent).
2. Any field that has jellyfish is equally likely to be either sparsely populated, in which case Spongebob will capture a measly 100 jellyfish, or densely populated, leading to a capture of 200 jellyfish.

Determine the probability mass function (pmf) of X, the total number of jellyfish Spongebob captures.

To report your answer, create two lists:

1. xi is the list of possible values that the pmf make take on
2. pxi is the list of respective probabilities for each value

So, for example if you determined the pmf to be:

p(0)=.15, p(1)=.25, p(2)=.35, p(3)=.2, p(4)=.05

Then you would give your answer as:

xi = [0, 1, 2, 3, 4]

pxi = [.15, .25, .35, .2, .05]

Answer 1