Chapter 9 Statistics Class 11 Notes
Important Notes of complete Chapter 9 Statistics Class 11 Notes written by Professor Mr. Faraz Qasir Suib. These notes are very helpful in the preparation of Chapter 9 Binomial and Hyper Geometric Probability Distribution 11 Notes 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:
- Here are the detailed class 11 statistics chapter 9 solutions to help you prepare for your exams.
- Define Bernoulli trials.
- Define random experiment.
- Define Binomial Probability Distribution.
- Define binomial experiment.
- What are the properties of binomial distribution?
- A random variable X has a binomial distribution with n = 5 and p = 0.2, find P(X = 2).
- Write down the formulas of mean, variance and standard deviation of binomial distribution.
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- A random variable ‘X’ is binomially distributed when n = 15 and p = 0.4. Find mean and variance of ‘X’.
- In binomial distribution, mean = 6 and Variance = 2.4, find parameters of binomial distribution.
- Find the number of trails of a binomial distribution which has mean = 12 and S.D = 2
- A coin is tossed 5 times. What is the probability of getting exactly 3 heads?
- What is Binomial frequency distribution.
- Define hyper geometric experiment.
- What are the properties of hyper geometric distribution?
- What is the Hypergeometric probability function?
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- What are the parameters of the hyper geometric distribution?
- Given N = 10, n = 4 and K = 5, find E(X).
- In a hyper geometric distribution N = 10, n = 2 and k = 3, find P(X=0)
- If N = 11, n = 5, k = 7, find variance of the hyper geometric distribution?
- If ‘x’ is a binomial random variable with n = 9 and p = 1/3, then find S.D.(3+2x)?
- In a binomial distribution mean = 36 and q = 0.83, find ‘n’ and ‘p’?
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- Introduction to Binomial and Hyper Geometric Probability Distribution: In an experiment of tossing a coin, drawing a card from a pack of playing cards repeatedly, etc., each drawing is called a trial. The results of each trial is classified as a success or failure. The probability of success is denoted, by p and the probability of failure is denoted by q where, q=1-p or q + p = 1. Let an experiment be repeated n times, the number of successes obtained in a trial of the experiment is denoted by x and the number of failures by n-x.
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- A trial having two possible outcomes i.e., only success and failure is called Bernoulli trials. For each bernoulli trial, the probability of success remains the same and the successive trials are independent.
- An experiment in which the outcomes can be classified as success or failure and in which the probability of success remains constant from trial to trial is called Binomial experiment. A binomial experiment possesses the following properties:
- i) Each trial of the experiment results in an outcome which can be classified into two categories i.e., success and failure.
- ii) The probability of success remains constant from one trial of the experiment to the next.
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- iii) The repeated trials are independent.
- iv) The experiment is repeated a fixed number of times.
- Binomial Probability Distribution: Suppose we have n independent trials for each of which the probability of success is p and the probability of failure is q and q+ p 1. The probability of exactly x success is given by.