Question

Let X be a discrete random variable whose value is given by the number of successes observed on a series of 10 Bernoulli trials in which the probability of success is 1/3. Which of the following statements is or are true?


I. X = B(10, 1/3)
II. The only possible values of X are the integers 1 through 10 inclusive.
III. If Y=10 - X, then Y = B(10, 2/3).

• A. I only

• B. I and II only

• C. I and III only

• D. all of I, II and III

• E. none of I, II or III

Answer 1

here since number of trails are fixed and probability is fixed and independent from trial to trail therefore X is binomial with parameter N and p=1/3

also Y =10-X , which follows binomial distribution with number of failures in sample of 10 with probability 2/3

X can take value of 0 as well therefore option II is incorrect

option C is correct : C. I and III only