Probability Class 10 Notes are prepared in such a way that they help get rid of any confusion among children regarding the course content since CBSE keeps on updating the course every year.

These notes are made highly experienced teachers strictly according to the NCERT Syllabus which offer the students a simple way to study or revise the chapter. Probability Class 10 Notes would provide you with an effective preparation for your board examinations. Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 where 0 indicates impossibility and 1 indicates certainty.

In mathematics, when next outcome of the experiment cannot be determined then we say it is a random experiment. A trial is an action which results in one or several outcomes, for example each toss of the coin and each throw of the die are called trials. Learn more about trails, experiments and events in Probability Class 10 Notes pdf.

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ECE 3530/CS 3130 - Engineering Probability and Statistics

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probability and statistics notes pdf

Class 6. Class 7. Class 8. Class 9. All Subjects. Class Informatics Practices.The population parameters are in general, not known and their estimates given by the corresponding sample statistic are used. Greek letters are used to denoted population parameters and Roman letters for sample statistic.

Sampling aims at gathering the maximum information about the population with the minimum effort, cost and time. The object of sampling studies is to obtain the best possible value of the parameters under specific conditions. Sampling determines reliability of these estimates. The logic of the sampling theory is the logic of induction in which we pass from a particular sample to general population.

Such a generalization from sample to population is called statistical inference. Consider all possible sample of size n which can be drawn from a given population at random.

For each sample, mean can be computed. The mean of the samples will not be identical. If these different means are grouped according of their frequencies, the frequency distribution so formed is called sampling distribution of the mean. Similarly sampling distribution of the standard deviation etc, can be obtained. When drawing each sample, the previous sample is put back so that the parent population remains the same. This is called sampling with replacement and all subsequent formulae will pertain to sampling with replacements.

It is used to assess the difference between expected and observed values. Standard deviation of the sampling distribution is called standard error S. Thus standard error of the sampling distribution of means is called standard error of means. The reciprocal of the standard error is called precision. The sampling distribution of large samples is assumed to be normal. Collection of all possible samples is population. It is impractical to collect data on each sample of a population.

Statistics helps to determine best estimate of the population parameter from randomly selected samples.

probability and statistics notes pdf

Because random errors are involved in determination of parameters, the estimate will represent a parameter with a given probability only. Sample Space : The set S of all possible outcomes of a given experiment is called sample space for the experiment.

An outcome an element of S, is called a sample point. Event : A subset of the sample space S is called an event. The set a consisting of a single sample point a in S is called elementary event.

Given two events A, B. Your email address will not be published. Notify me of follow-up comments by email. Notify me of new posts by email. Related Books. Leave a Reply Cancel reply Your email address will not be published.

probability and statistics notes pdf

Please like our FB Page for instant updates.To browse Academia. Skip to main content. Log In Sign Up. Notes on Probability Theory and Statistics. Negesse Yilmma. The biggest possible collection of points under consideration is called the space, universe, or universal set. For Probability Theory the space is called the sample space. Disjoint or mutually exclusive sets are the sets that their intersection is the empty set, i. Subsets A1A2Uncertainty or variability are prevalent in many situations and it is the purpose of the probability theory to understand and quantify this notion.

The basic situation is an experiment whose outcome is unknown before it takes place e. The sample space is the collection or totality of all possible outcomes of a conceptual experiment. An event is a subset of the sample space.

Let us describe the sample space S, i. Example: Consider the drawing an ace event A from a deck of 52 cards. What is P A? Notice that the a priori probability is in this case 0. Subjective Probability: This is based on intuition or judgment.

We shall be concerned with a priori probabilities. These probabilities involve, many times, the counting of possible outcomes. The sample space in both cases, although discrete, can be quite large and it not feasible to write out all possible outcomes. Duplication is permissible and Order is important Multiple Choice Arrangementi.

Example: Find all possible combinations of the letters A, B, C, and D when duplication is allowed and order is important. Duplication is not permissible and Order is important Per- mutation Arrangementi. In this case where we want to permute n objects in x places the possible outcomes is given from: n! Example: Find all possible permutations of the letters A, B, C, and D when duplication is not allowed and order is important.

Duplication is not permissible and Order is not important Combination Arrangementi. A is an algebra if 1. These are some pretty nasty ones like the Cantor set. P is a matter of choice and will depend on the problem. In many discrete cases, the problem can usually be written such that outcomes are equally likely.Conditional Probability. Permutations nPr for Multiple Subsets. Sample Size by Standard Deviation.

Statistics: Lecture Notes

Sample Size by Proportion. Population Variance Estimation. Population Variance. Standard Deviation. Population Standard Deviation. Z-Test for Proportion Significance. Students t-Test for Mean Significance. F-Test between Sample Variances. CHI-squared Test.

Standard or Z-Score. SE of Observed Sample Proportion. SE of difference between 2 sample proportions. Confidence Interval for Mean - Infinite Population. Confidence Interval for Mean - Finite Population. CI for Proportion - Infinite Population. CI for Proportion - Finite Population. Margin of Error. Correlation Coefficient. Linear Regression. Coefficient of Variation. Normal Probability Distribution. Poisson Probability Distribution.One of the most familiar uses of statistics is to determine the chance of some occurrence.

For instance, what are the chances that it will rain tomorrow or that the Chicago Cubs will win a World Series? These kinds of probabilities, although interesting, are not the variety under discussion here. Rather, we are examining the probability in statistics that deals with classic theory and frequency theory—events that can be repeated over and over again, independently, and under the same conditions.

Coin tossing and card drawing are two such examples. A fair coin one that is not weighted or fixed has an equal chance of landing heads as landing tails. A typical deck of cards has 52 different cards—13 of each suit hearts, clubs, diamonds, and spades —and each card or suit has an equal chance of being drawn. This kind of event forms the basis of your understanding of probability and enables you to find solutions to everyday problems that seem far removed from coin tossing or card drawing.

Probability helps us describe our conclusions in a way that takes the uncertainty from random sampling into account. Previous Comparing Results. Next Quiz Introduction to Statistics. Removing book from your Reading List will also remove any bookmarked pages associated with this title. Are you sure you want to remove bookConfirmation and any corresponding bookmarks? My Preferences My Reading List. Home Study Guides Statistics Probability. Adam Bede has been added to your Reading List!If ALL your links come from these type of sources, and are created in a manipulative way that could be seen as a problem.

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Probability and Statistics - PS Study Materials

Link building in 2017 is the process of earning links on other websites. Find Out More How Many Words In ALT Text For Google. REDDIT USERS: How Do You Rank Top In Google. Click here to get your SEO plan delivered in 5 working days. Download Your Free Seo Training Ebook. The shared links from Fan pages are treated similarly to Twitter links.Technically, we're also seeing that with nearly every Soviet ship. The Soviets didn't name classes after one of the ships in the class.

They named them after a project number. For example Gnevny was the first ship of her class, but the Soviets never called it the Gnevny class. They called it Project 7. Tech tree could get the 1941 rebuild easily enough. HMS Duke of York or HMS Prince of Wales. Maybe HMS Glorious before she was converted to an aircraft carrier.

Campbelltown is nice and all but it would be good to have a proper RN destroyer. Maybe a French Cruiser. Would like to see a German dd premium. Probably going to get the Hood and Alabama(duh). Maybe a RN DD. Really going to depend on the future lines they unveil. Those could be used in such a line. We don't currently have a British heavy cruiser in game and Exeter is probably the most famous of those ships so would be a good choice to introduce them.

Also 2017 is the 75th anniversary of the battles of the Java sea. So if WG wanted to do an event then, they could have a nice premium ship to release at the same time. But I think with the Indy there's no point.

There is always going to be overlap. The ship may be a different tier, or have some other characteristics that make it different. Didn't she was the same as the Richelieu. I think the US refit of Richelieu would be better as a premium but as it's head of class and Dunkerque, already in the game (also head of class) it won't happen.

They won't put two of the last french BBs as premiums if they want to make a french BB line (they have the material). In term of unique flavor, Jean Bart would be the very same as stock Richelieu, that's why I don't understand it as a Premium choice. Richelieu all the way. That US AA refit.

It will be god tier. Gascogne would've had two turrets like Richelieu and Jean Bart but with one facing forward and one facing aft. The armor is rather weak already, why make it worse by showing more broadside to have the aft turret shoot.

It's Graf Spee all over again. Why loose the flavor and strenght of the full frontal turrets. I don't know if the Jean Bart offers something sufficiently different or special to sell it while having the ship's class in the tech tree. But there's the Prinz Eugen, so t could happen. Weaknesses would be it's lacking long range AA, low number of secondaries, and, despite supercharges, still sporting just 8 15 inch guns at T8.

Guessing that she will also get a radar consumable due to being the last Battleship ever built (Jean Bart really doesn't count).

For this reason, sources which quote HMS Vanguard as having gun ranges in excess of 32,000 yards (29,260 m) are somewhat misleading, as such a range would have required the use of super charges, which she never carried. She was a Franken-ship made from spare hull and guns, although she was built I think her strange construction could easily lend to creative balancing.

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