Probability Distribution of a Random Variable - Probability, Class 12, Math

# Probability Distribution of a Random Variable - Probability, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Probability Distribution of a Random Variable - Probability, Class 12, Math Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is a probability distribution of a random variable?
Ans. A probability distribution of a random variable is a mathematical function that describes the likelihood of different outcomes occurring for that random variable. It assigns probabilities to each possible value that the random variable can take.
 2. What is the difference between a discrete and a continuous probability distribution?
Ans. A discrete probability distribution is one where the random variable takes on a finite or countably infinite number of distinct values, such as the number of heads in a coin toss. A continuous probability distribution, on the other hand, is one where the random variable can take on any value within a certain range, such as the height of individuals in a population.
 3. How can we represent a probability distribution?
Ans. A probability distribution can be represented in various ways. One common representation is through a probability mass function (PMF) for discrete random variables, which assigns probabilities to each possible value. For continuous random variables, a probability density function (PDF) is used, which gives the relative likelihood of the random variable falling within a particular interval.
 4. What are some important properties of a probability distribution?
Ans. Some important properties of a probability distribution include: - The sum of the probabilities for all possible values of the random variable must equal 1. - The probability for any specific value of the random variable must be between 0 and 1. - The probabilities for different values of the random variable must be non-negative. - The probability distribution can be used to calculate expected values, variances, and other summary statistics of the random variable.
 5. How can we use a probability distribution to make predictions or decisions?
Ans. A probability distribution allows us to quantify the likelihood of different outcomes, which can be used to make predictions or decisions. For example, if we have the probability distribution of the number of defective items in a batch, we can calculate the expected number of defects and make decisions regarding quality control. Additionally, probability distributions can be used in statistical inference to make inferences about population parameters based on sample data.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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