1. Math
  2. Statistics And Probability
  3. 3 18 pts let ya and y denote bernoulli random...

Question: 3 18 pts let ya and y denote bernoulli random...

Question details

(3) 18 pts] Let Ya and Y, denote Bernoulli random variables from two different populations, denoted a and b. Suppose that E(%)-Pa and E(%)-pb. A random sample of size na is chosen from population a, with sample average denoted pa, and a random sample of size nb is chosen from population b, with sample average denoted Suppose the sample from population a is independent of the sample from population b (a) Show that E(Pi) Pi and var(Pi)-P( pi)/n, for j E ta, b (b) Show that var(Pa P) var(Pa) +var(Pb) (HINT remember that the samples are inde- pendent) (c) Suppose that n and nb are large. Show that a 95% confidence interval for the quantity (pa-p.) is given by (pa-pb) (d) How would you construct a 90% confidence interval for (pa-Pb)?

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution