Quiz Space

Statistics for Data Science II · End Term · 10 May 2026 · January 2026 term

Question 45: A box contains some green balls and some yellow balls. M…

Question 45

+1 markWritten answer

A box contains some green balls and some yellow balls. Meera claims that if a ball is picked randomly from the box, then the probability that the ball will be green is 0.25. Arjun suspects that this probability is too high. To test the claim, he randomly picks 8 balls from the box. If two or more green balls are obtained among the 8 balls, then he accepts Meera's claim; otherwise, he rejects it. Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

See the whole paperTake it as a mock test

Question 45 of 51 in the IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 10 May 2026, in the January 2026 term (Statistics2 06 May 26). It carries 1 mark.

More questions from this paper

  1. Q1Figure question
  2. Q2Figure question
  3. Q3Suppose are i.i.d random variables with E[ ]= and Var( = for . Let be an estimator of . Find the mean squared error (MS…
  4. Q4Let . The prior distribution of has the following PMF: Consider the samples S: { }. Find the posterior probability usin…
  5. Q5The probability density function of a random variable is given as Find the value of .
  6. Q6Let be a sample from a normal distribution having a variance of 25. We wish to test the hypothesis against . Consider a…
  7. Q7A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  8. Q8The time (in minutes) passengers spend in the airport security line during a quiet period follows a continuous uniform …
  9. Q9A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  10. Q10Let be a discrete random variable with PMF as follows: Suppose i.i.d. . Define a new random variable . Which of the fol…
  11. Q11A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  12. Q12Let be i.i.d. samples from and be i.i.d. samples from . The observed sample means are and . We wish to test the hypothe…
  13. Q13A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  14. Q14Let be a discrete random variable with probability mass function: Consider the random sample {1, 2, 1, 2}. Assume that …
  15. Q15A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  16. Q16Let be a discrete random variable with probability mass function: Consider the random sample {1, 2, 1, 2}. Assume that …
  17. Q17Let be i.i.d. samples from and be i.i.d. samples from . The observed sample means are and . We wish to test the hypothe…
  18. Q18Let be a discrete random variable with PMF as follows: Define another random variable . Based on the above data, answer…
  19. Q19Let be a discrete random variable taking values {1, 2, 3} with respective probabilities , where is a parameter. Conside…
  20. Q20Let be a discrete random variable with PMF as follows: Define another random variable . Based on the above data, answer…
  21. Q21Let be a discrete random variable with probability mass function: Consider the random sample {2,3,1}. Assume that the p…
  22. Q22The joint PDF of two random variables and is given by Based on the above data, answer the given subquestions. Find the …
  23. Q23Let be a discrete random variable with probability mass function: Consider the random sample {2,3,1}. Assume that the p…
  24. Q24The joint PDF of two random variables and is given by Based on the above data, answer the given subquestions. Find the …
  25. Q25A discrete random variable has the following probability mass function : Based on the above data, answer the given subq…
  26. Q26Define the null hypothesis and the alternative hypothesis.
  27. Q27A discrete random variable has the following probability mass function : Based on the above data, answer the given subq…
  28. Q28Find the significance level of the test. Enter the answer correct to three decimal places.
  29. Q29Find the method of moments estimate of for the given sample. Enter the answer correct to one decimal place.
  30. Q30Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  31. Q31The experiment is considered efficient if the expected number of trials required to achieve the outcome is at most 4. U…
  32. Q32Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  33. Q33Define the null hypothesis and the alternative hypothesis.
  34. Q34Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  35. Q35Find the significance level of the test. Enter the answer correct to three decimal places.
  36. Q36Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  37. Q37Find the value of for which . Enter the answer correct to one decimal place.
  38. Q38Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  39. Q39Find . Enter the answer correct to two decimal places.
  40. Q40Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…
  41. Q41A pharmaceutical company produces vaccine vials, and historically, the probability that a vial is defective is . A new …
  42. Q42Let be a discrete random variable with probability mass function: Consider the random sample {2,3,1}. Assume that the p…
  43. Q43A discrete random variable has the following probability mass function : Based on the above data, answer the given subq…
  44. Q44Let the random variable represent the number of trials required to achieve a certain outcome in an experiment, where {1…
  45. Q46Suppose . Based on the above data, answer the given subquestions.
  46. Q47Let be a discrete random variable with probability mass function: Consider the random sample {1, 2, 1, 2}. Assume that …
  47. Q48Let be a discrete random variable with PMF as follows: Define another random variable . Based on the above data, answer…
  48. Q49The joint PDF of two random variables and is given by Based on the above data, answer the given subquestions.
  49. Q50A factory produces light bulbs. The manufacturer claims that the probability that a randomly selected bulb is defective…
  50. Q51Let be a random variable with mean and variance . Let and be the sample means of two independent random samples of size…