Probability distributions are used to model the probability of occurrence of different outcomes in an experiment or random event. The Class 12 Mathematics syllabus covers the following topics related to probability distributions:
Random Variables: This topic covers the concept of random variables, discrete and continuous random variables, probability mass function, probability density function, and cumulative distribution function.
Bernoulli Trials and Binomial Distribution: This topic covers the concept of Bernoulli trials, binomial distribution, and the properties of binomial distribution.
Poisson Distribution: This topic covers the concept of Poisson distribution, its properties, and its applications.
Normal Distribution: This topic covers the concept of normal distribution, standard normal distribution, and its properties.
Markov’s Inequality and Chebyshev’s Inequality: This topic covers the concept of Markov’s inequality and Chebyshev’s inequality, which provide bounds on the probability of a random variable deviating from its mean.
Probability distributions are important because they provide a mathematical framework for analyzing and predicting the behavior of random events. The concept of random variables is used in various fields such as finance, economics, engineering, and science to model and analyze the behavior of uncertain events. The properties of binomial distribution are used in solving problems related to coin tossing, while the properties of Poisson distribution are used in solving problems related to the occurrence of rare events. The concept of normal distribution is used in statistics to model and analyze data in various fields such as finance, engineering, and science. The inequalities of Markov and Chebyshev are used in estimating the probability of a random variable deviating from its mean, which is important in risk management and decision-making.