Chapter 8 Statistics Class 11 Notes
Important Notes of complete Chapter 8 Statistics Class 11 Notes written by Professor Mr. Faraz Qasir Suib. These notes are very helpful in the preparation of Chapter 8 Probability Distributions 11 Notes PDF for the students of the intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
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- What is a random variable?
- Define continuous and discrete random variable.
- What is distribution function of a discrete random variable X?
- Define probability density function.
- What are the properties of discrete probability distribution?
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- What is meant by mathematical expectation of a random variable?
- Enlist properties of expectations.
- Given X = 0, 1, 2 and P(X) = 9/16, 6/16, 1/16, find variance of X.
- Given the probability distribution. Find K
- Given that f(x) = x/10, x = 1, 2, 3, 4. Show that f(x) is a probability function.
- Given E(X) = 0.63 and Var(X) = 0.2331 then find E(X2 ).
- Given X = 1, 2, 3, 4, 5 and P(X) = 1/10, 3/10, P, 2/10, 1/10. Find the value of P.
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- Find the probability distribution of the number of heads when two coins are tossed.
- Define random experiment.
- Enlist properties of probability mass function.
- If E(X) = 1.4, then find E(5x – 4).
- Given: E(x) = 0.56, var(x) = 1.36 and if y =2x + 1, then find E(y) and var(y).
- Introduction to Probability Distributions: Whenever we talk about random experiments, there is the need to associate a numerical value with each of their outcomes, in order to study them. As a result, two types of variables arise. i. Discrete random variable. ii. Continuous random variable.
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- A discrete random variable almost always arises in connection with counting and a continuous random variable is one whose values are typically obtained by measurements.
- In case of a discrete random variable, its probability distribution describes how much of the probability is placed on each of its possible values with the total of all these probabilities equal to 1. The probability distribution of a discrete random variable is usually called its probability mass function.
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- In case of a continuous random variable, we cannot talk about the probability on a point instead we talk about the probability on any interval of the values the random variable takes, with the total of the probabilities equal to 1. The probability distribution of a continuous random variable is called its probability density function.
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- The probability distribution of a discrete random variable is usually written with the help of a function, called its formula or it can be described with the help of a two column table (like frequency distribution) where one column gives the values (intervals of values in case of continuous random variables) and the other column gives the probabilities.
- Probability Mass Function: As the value of a discrete random variable is determined by the outcome of a random experiment, one can associate with each possible value of the discrete random variable a probability that a random variable will take on that value.
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- The probability mass function of a discrete random variable Y describes the values of Y and the probability associated with each value of Y. Usually, it is written in a two column table where one column gives the values of the random variable Y and the other column gives the probabilities associated with each value.