1. How many possible permutations can be formed from the word ‘statistics’? 2. In how many ways can a team of 11 players be chosen from a total of 16 players? 3. State multiplicative theorem of probability for dependent events. 4. An aptitude test with 4 options. If a student marks the options of the questions randomly and independently, then find the probability of being correct to 4 questions. 5. A can solve 75% questions in a book and B can solve 60% questions in that book. Find the probability that randomly selected questions is solved by them? 6. What is the probability of getting at least 2 heads when 3 coins are tossed? 7. Find P(A ∩ B) if P(A) = ¼ and P(B) = 1/3 and p(A U B) = ½ . 8. State the laws of expectation.
9. Describe the properties of discrete probability distribution. 10. Given E(X) = 0.55, Var(X) = 1.55 and Y = 2X + 1. Find E(Y) and Var(Y). 11. Show that the mean of the binomial distribution (q + p)2 is 2p. 12. Show that mean is 2p and σ2 = 2pq for a binomial distribution in which n = 2. 13. A random variable X has a binomial distribution with E(X) = 2.4 and p = 0.3. Find the standard deviation of X. 14. Describe the normal distribution and write down its equation. 15. What is standard normal variable?
16. The value 2nd moment about mean in a normal distribution is 5. Find the 3rd and 4th moment about mean for this distribution. 17. Is every symmetrical distribution a normal distribution? 18. What is the relation between the binomial and normal distribution? 19. Define sampling units and frame.
20. What is the difference between sampling and non-sampling error? 21. Name the four techniques used in probability sampling. 22. Given P1 = 2/3, n1 = 2, P2 = 2, n2 = 2. Find µP1-P2 and σP1 – P2. 23. What is the difference between sampling with replacement and without replacement? 24. Find 90% confidence interval of µ from a sample...