Quiz1

Statistics for Data Science II · Quiz 1 · May 2026

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 2 MCQ · 0.0 marks

[[IMAGE:91c5350eed0f5ff1_2_2]] [[IMAGE:91c5350eed0f5ff1_3_3]]

Useful Data has been mentioned above.
This data attachment is just for a reference & not for an evaluation.

A published solution is not available for this question yet.

Question 3 NAT · 3.0 marks

Let X be a continuous random variable with PDF as follows: [[IMAGE:91c5350eed0f5ff1_4_4]] Find the value of a.

A published solution is not available for this question yet.

Question 4 NAT · 3.0 marks

Let [[IMAGE:91c5350eed0f5ff1_4_5]] and [[IMAGE:91c5350eed0f5ff1_4_6]] be two independent random variables such that [[IMAGE:91c5350eed0f5ff1_4_7]] [[IMAGE:91c5350eed0f5ff1_4_8]] [[IMAGE:91c5350eed0f5ff1_4_9]] Let another random variable [[IMAGE:91c5350eed0f5ff1_4_10]] be defined as [[IMAGE:91c5350eed0f5ff1_4_11]] Find the value of [[IMAGE:91c5350eed0f5ff1_4_12]] Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 5 NAT · 3.0 marks

A number from 00 to 99 is selected uniformly at random.The numbers 0 to 9 are treated as two digit numbers and denoted as 00 to 09. Let, • [[IMAGE:91c5350eed0f5ff1_4_13]] be the digit in the units place, • [[IMAGE:91c5350eed0f5ff1_4_14]] be the remainder when the number is divided by 4. Find the value of [[IMAGE:91c5350eed0f5ff1_4_15]] . Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 6 NAT · 3.0 marks

A random variable [[IMAGE:91c5350eed0f5ff1_5_16]] has mean 10 and variance 9. Using Chebyshev's inequality, find a lower bound on [[IMAGE:91c5350eed0f5ff1_5_17]] . Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 7 NAT · 3.0 marks

A shopping mall issues 400 lucky draw coupons. Among them, one coupon is worth a gift voucher of Rs 2000, one coupon is worth a gift voucher of Rs 1000, and all other coupons are worth Rs 0. If a customer receives 2 coupons drawn at random from the 400, what is the expected value (in Rs) of the prizes won by the customer?

A published solution is not available for this question yet.

Question 8 MCQ · 3.0 marks

Let [[IMAGE:91c5350eed0f5ff1_6_18]] be a discrete random variable with PMF [[IMAGE:91c5350eed0f5ff1_6_19]] Based on the above data, answer the given subquestions.

Find the value of [[IMAGE:91c5350eed0f5ff1_6_20]]

[[IMAGE:91c5350eed0f5ff1_6_21]]
[[IMAGE:91c5350eed0f5ff1_6_22]]
[[IMAGE:91c5350eed0f5ff1_6_23]]
[[IMAGE:91c5350eed0f5ff1_6_24]]

A published solution is not available for this question yet.

Question 9 NAT · 2.0 marks

Let [[IMAGE:91c5350eed0f5ff1_6_18]] be a discrete random variable with PMF [[IMAGE:91c5350eed0f5ff1_6_19]] Based on the above data, answer the given subquestions.

Using Markov's inequality, obtain an upper bound for [[IMAGE:91c5350eed0f5ff1_6_25]] Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 10 MCQ · 2.0 marks

Let the random variables [[IMAGE:91c5350eed0f5ff1_7_26]] i.i.d Uniform{1, 2, 3, 4}. Based on the above data, answer the given subquestions.

What is the value of [[IMAGE:91c5350eed0f5ff1_7_27]] ?

[[IMAGE:91c5350eed0f5ff1_7_28]]
[[IMAGE:91c5350eed0f5ff1_7_29]]
[[IMAGE:91c5350eed0f5ff1_7_30]]
[[IMAGE:91c5350eed0f5ff1_7_31]]

A published solution is not available for this question yet.

Question 11 NAT · 3.0 marks

Let the random variables [[IMAGE:91c5350eed0f5ff1_7_26]] i.i.d Uniform{1, 2, 3, 4}. Based on the above data, answer the given subquestions.

Let [[IMAGE:91c5350eed0f5ff1_7_32]] find the value of [[IMAGE:91c5350eed0f5ff1_7_33]] Enter the answer correct to three decimal places.

A published solution is not available for this question yet.

Question 12 MCQ · 3.0 marks

Let [[IMAGE:91c5350eed0f5ff1_8_34]] be i.i.d random variables with the following probability mass function [[IMAGE:91c5350eed0f5ff1_8_35]] Based on the above data, answer the given subquestions.

Find the value of [[IMAGE:91c5350eed0f5ff1_8_36]] .

[[IMAGE:91c5350eed0f5ff1_8_37]]
[[IMAGE:91c5350eed0f5ff1_8_38]]
[[IMAGE:91c5350eed0f5ff1_8_39]]
[[IMAGE:91c5350eed0f5ff1_8_40]]

A published solution is not available for this question yet.

Question 13 MCQ · 2.0 marks

Let [[IMAGE:91c5350eed0f5ff1_8_34]] be i.i.d random variables with the following probability mass function [[IMAGE:91c5350eed0f5ff1_8_35]] Based on the above data, answer the given subquestions.

Find the value of [[IMAGE:91c5350eed0f5ff1_8_41]] .

[[IMAGE:91c5350eed0f5ff1_9_42]]
[[IMAGE:91c5350eed0f5ff1_9_43]]
[[IMAGE:91c5350eed0f5ff1_9_44]]
[[IMAGE:91c5350eed0f5ff1_9_45]]

A published solution is not available for this question yet.

Question 14 NAT · 3.0 marks

Let [[IMAGE:91c5350eed0f5ff1_9_46]] be i.i.d samples of a discrete random variable [[IMAGE:91c5350eed0f5ff1_9_47]] whose PMF is as follows: [[IMAGE:91c5350eed0f5ff1_9_48]] Based on the above data, answer the given subquestions.

What is the probability that 1 appears exactly once in the samples? Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 15 NAT · 2.0 marks

What is the probability that none of the four samples is equal to 0? Enter the answer correct to two decimal places.

A published solution is not available for this question yet.

Question 16 NAT · 1.0 marks

Suppose that the time [[IMAGE:91c5350eed0f5ff1_10_49]] (in minutes) that a customer waits at a service counter is a random variable with probability density function [[IMAGE:91c5350eed0f5ff1_10_50]] Let [[IMAGE:91c5350eed0f5ff1_10_51]] be the event that a person has to wait for more than 2 minutes and [[IMAGE:91c5350eed0f5ff1_10_52]] be the event that he has to wait for more than 1 minute. Find the value of [[IMAGE:91c5350eed0f5ff1_10_53]] . [[IMAGE:91c5350eed0f5ff1_11_54]]

Enter the correct option number for [[IMAGE:91c5350eed0f5ff1_11_55]] .