2017 Statistics Paper - I

Leela has appeared in an examination which follows multiple choice questions, each having five possible answers. The probability that she knows an answer is 0·75. If she does not know an answer, she will guess, with the conditional probability \( 1/5 \) of being correct. The conditional probability that Leela knows the answer, given that she gives the correct answer, is

Consider a sequence of Bernoulli trials with probability of success \( 1/3 \) for each trial. Let X denote the length of run of either successes or failures starting with the first trial. Then the value of E(X) is

The probability that a death occurs due to heart failure is 0·45 and the probability that a death occurs due to cancer is 0·22. Consider the following statements : 1. The probability that the death is either due to heart failure or due to cancer is 0·67. 2. The probability that the death is due to some other cause (but not these two) is 0·55. Which of the statements is/are correct ?

Let X, a continuous random variable, follow U(0, 1) distribution. Then, we assert that 1. P(X ≥ 0·27) = 0·73 2. P(0·27 < X < 1·27) = 0·73 Which of the above assertions is/are correct ?

Let X be the number of phone calls received at a call centre during business hours and Y be the number of calls received outside business hours, on a particular day. Assume that X and Y are independent, and follow the Poisson distribution with means \( \lambda₁ \) and \( \lambda₂ \) respectively, where \( \lambda₁ \neq \lambda₂ \). Then the conditional distribution of X, given the total number of calls received that day (i.e., X + Y), is

A and B are events such that P(A) = 1/4, P(B) = 1/3 and P(A ∩ B) = 1/12. Then consider the following: 1. P(A ∩ B̅) = 1/4 2. P(A̅ ∩ B) = 1/2 3. P(B | A̅) = 1/3 Which of the above statements are correct?