Pre-Quiz - Basic Statistics

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This quiz is based on pre-requisites for the last topic of data science module. You should be able to finish this quiz in 10-15 minutes.

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A box contains 10 black balls and 5 red balls. Two balls are drawn at random at a time and the colours of them are noted, and then they are put back. What is the probability that one of them is black and one of them is red? *

1 point

2/9

5/21

4/9

10/21

A and B are two independent events. Let P(E) denote the probability of an event. Suppose P(A) = 0.3 and P(B) = 0.2. Find P(A U B'). (E' denotes the complement of an event) *

1 point

0.06

0.44

0.86

0.24

The standard deviation of a random variable X ~ Poisson(p) is *

1 point

p^2

p^0.5

p^-0.5

Five percent of patients suffering from a certain disease is selected to undergo a new treatment that is believed to increase the recovery rate from 30 percent to 50 percent. A person is randomly selected from these patients after the completion of the treatment and is found to have recovered. What is the probability that the patient received the new treatment? *

1 point

3/62

5/62

0.3

0.5

A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb in the box is 0.1, and the probability that there are at least 2 defective bulbs is 0.05. Then find the probability that the box contains no defective bulbs. *

1 point

0.1

0.05

0.9

X is a random variable such that X ~ N(a,b). Then 7X ~ *

1 point

N(a,b)

N(7a,7b)

N(7a,49b)

N(a,7b)

A regular dice is rolled twice. What is the probability that the value shown up in the second roll is 3 given the value obtained in first roll is 2? *

1 point

1/36

1/6

2/36

Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A? *

1 point

44/69

25/69

11/69

13/24

Suppose we have a sample of N observations a1,a2,a3,a4,...,aN. The sample variance is given by? (symbols used have their usual meaning) *

1 point

Option 1

Option 2

Option 3

Option 4

I throw a die and get $1 if it is showing 1, and get $2 if it is showing 2, and get $3 if it is showing 3, etc. What is the amount of money I can expect if I throw it 100 times?

1 point

250

500

None of them

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