Mathematics

Probability Distributions

457 Questions

Probability distributions describe the likelihood of different outcomes in a statistical experiment. Key topics include calculating confidence intervals, understanding Type II errors, and working with the standard normal distribution. These concepts are frequently tested in mathematics and statistics sections of various competitive exams.

Standard normal distributionType II error probabilityConfidence interval interpretationPoisson distributionProbability density function

Probability Distributions Questions

Multiple choice

What is the probability of an event in a probability space?

  1. The ratio of the number of favorable outcomes to the total number of possible outcomes.

  2. The ratio of the number of unfavorable outcomes to the total number of possible outcomes.

  3. The difference between the number of favorable outcomes and the number of unfavorable outcomes.

  4. None of the above.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of an event in a probability space is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

Multiple choice

Which of the following is an example of a probability distribution?

  1. The uniform distribution.

  2. The normal distribution.

  3. The binomial distribution.

  4. All of the above.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability distributions are functions that assign probabilities to events in a probability space. Examples of probability distributions include the uniform distribution, which assigns equal probability to all outcomes in a sample space, the normal distribution, which is a bell-shaped curve that is often used to model continuous random variables, and the binomial distribution, which is used to model the number of successes in a sequence of independent experiments.

Multiple choice

The 'Vyavahara Bija Ganita' of Lilavati provides a method for calculating the 'vyavahara bija', which is a measure of the risk associated with a particular hazard. What is the formula for calculating the vyavahara bija?

  1. Vyavahara bija = (Likelihood of occurrence) x (Severity of consequences)

  2. Vyavahara bija = (Likelihood of occurrence) + (Severity of consequences)

  3. Vyavahara bija = (Likelihood of occurrence) / (Severity of consequences)

  4. Vyavahara bija = (Likelihood of occurrence) - (Severity of consequences)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the vyavahara bija is Vyavahara bija = (Likelihood of occurrence) x (Severity of consequences). The likelihood of occurrence is a measure of how likely it is that the hazard will occur, while the severity of consequences is a measure of the potential consequences of the hazard occurring.

Multiple choice

Which mathematical concept is used to describe the probability of an event occurring?

  1. Probability

  2. Statistics

  3. Calculus

  4. Geometry
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability is a mathematical concept that quantifies the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).

Multiple choice

The probability of selecting any member of the population is the same in:

  1. Simple Random Sampling

  2. Systematic Sampling

  3. Stratified Sampling

  4. Cluster Sampling
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In simple random sampling, the probability of selecting any member of the population is the same.

Multiple choice

What is the probability of an event occurring if it has a 30% chance of happening?

  1. 0.3

  2. 0.6

  3. 0.7

  4. 0.9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of an event occurring is the likelihood of it happening. In this case, the probability of the event occurring is 30%, which is equal to 0.3.

Multiple choice

What is the ergodicity property of a Markov Chain?

  1. The property that the Markov Chain will eventually reach a stationary distribution.

  2. The property that the Markov Chain will never reach a stationary distribution.

  3. The property that the Markov Chain will reach a stationary distribution only if it starts in a certain state.

  4. The property that the Markov Chain will reach a stationary distribution only if it starts in a certain set of states.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ergodicity property of a Markov Chain states that the chain will eventually reach a stationary distribution, regardless of the initial state.

Multiple choice

What is the probability that a randomly selected person in India will travel by bus?

  1. 0.25

  2. 0.5

  3. 0.75

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 75% of all passenger trips in India are made by bus.

Multiple choice

What is the probability that a randomly selected person in India will travel by train?

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Railways, approximately 20% of all passenger trips in India are made by train.

Multiple choice

What is the probability that a randomly selected person in India will travel by air?

  1. 0.05

  2. 0.1

  3. 0.15

  4. 0.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the Directorate General of Civil Aviation, approximately 5% of all passenger trips in India are made by air.

Multiple choice

What is the probability that a randomly selected person in India will travel by car?

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 20% of all passenger trips in India are made by car.

Multiple choice

What is the probability that a randomly selected person in India will travel by bicycle?

  1. 0.05

  2. 0.1

  3. 0.15

  4. 0.2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 10% of all passenger trips in India are made by bicycle.

Multiple choice

What is the probability that a randomly selected person in India will travel by foot?

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 25% of all passenger trips in India are made by foot.

Multiple choice

What is the probability that a randomly selected person in India will travel by more than one mode of transportation?

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 20% of all passenger trips in India involve more than one mode of transportation.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is not listed in the options?

  1. 0.01

  2. 0.02

  3. 0.03

  4. 0.04
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are a number of modes of transportation that are not listed in the options, such as rickshaws, tongas, and bullock carts. According to the Indian Ministry of Road Transport and Highways, approximately 2% of all passenger trips in India are made by these modes of transportation.