Question

Suppose that a patient with heart attack dies of the attack with probability 0.05, and the survival of the patients are independent of each other. Now we have 5 patients who suffer heart attack.

1. 1. (2 points) Let Y be the number of patients that will survive. What is the distri- bution of Y ? (Please clearly give the name of the distribution and specify relevant parameters.)
2. 2. (2 points) what is the probability that all of the 5 patients will survive？
3. 3. (2 points) What is the expected number of patients that will survive?

Answer 1

• Y is the number of patients that will survive out of 5 patients.
  The probability of success is: 1 - 0.5 = 0.95.
  Again, each patients are independent.
  
  Clearly,
  The p.m.f. is given by:
  

• Here, we are to find that all of them will survive:
  
  
  
  
  

• The expectation of distribution is: .
  
  Hence,
  
  
  

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