Answer:
The cumulative distribution is:
P(X=0)=0.11291
P(X≤1)=0.94788
P(X≤2)=0.99921
P(X≤3)=1.00000
Step-by-step explanation:
First, we can write the sample space for X
For X=0:
- There is one combination possible (no one dies).
- The probability is
For X=1:
- There are 3 combinations possible, one for each person (one death). One combination has different probability than the other (when the person with three risk factor dies).
- The probability is:
For X=2:
- There are 3 combinations, with different probabilities (two persons die).
- The probability is:
For X=3:
- There is only one combination (the three persons die)
- The probability is:
The cumulative distribution is:
P(X=0)=0.11291
P(X≤1)=0.11291+0.83498=0.94788
P(X≤2)=0.94788+0.05132=0.99921
P(X≤3)=0.99921+0.00079=1.00000