File Name: statistics and probability formulas .zip
Conditional Probability. Permutations nPr for Multiple Subsets. Sample Size by Standard Deviation.
This means that over the long term of doing an experiment over and over, you would expect this average. If you repeat this experiment toss three fair coins a large number of times, the expected value of X is the number of heads you expect to get for each three tosses on average. It represents the mean of a population.
A men's soccer team plays soccer zero, one, or two days a week. The probability that they play zero days is. X takes on the values 0, 1, 2.
In this column, you will multiply each x value by its probability. The men's soccer team would, on the average, expect to play soccer 1. The number 1. As you learned in Chapter 3 , if you toss a fair coin, the probability that the result is heads is 0. This probability is a theoretical probability, which is what we expect to happen.
This probability does not describe the short-term results of an experiment. If you flip a coin two times, the probability does not tell you that these flips will result in one head and one tail. Even if you flip a coin 10 times or times, the probability does not tell you that you will get half tails and half heads. The probability gives information about what can be expected in the long term. To demonstrate this, Karl Pearson once tossed a fair coin 24, times!
He recorded the results of each toss, obtaining heads 12, times. In his experiment, Pearson illustrated the law of large numbers. The law of large numbers states that, as the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency approaches zero the theoretical probability and the relative frequency get closer and closer together.
The relative frequency is also called the experimental probability, a term that means what actually happens. In the next example, we will demonstrate how to find the expected value and standard deviation of a discrete probability distribution by using relative frequency.
Like data, probability distributions have variances and standard deviations. Both are parameters since they summarize information about a population. The formulas are given as below. The researcher randomly selected 50 new mothers and asked how many times they were awakened by their newborn baby's crying after midnight per week. Two mothers were awake zero times, 11 mothers were awake one time, 23 mothers were awake two times, nine mothers were awake three times, four mothers were awakened four times, and one mother was awake five times.
Find the expected value of the number of times a newborn baby's crying wakes its mother after midnight per week. Calculate the standard deviation of the variable as well. X takes on the values 0, 1, 2, 3, 4, 5. Construct a PDF table as below.
The column of P x gives the experimental probability of each x value. We will use the relative frequency to get the probability. For example, the probability that a mother wakes up zero times is 2 50 2 50 since there are two mothers out of 50 who were awakened zero times. The third column of the table is the product of a value and its probability, x P x. Therefore, we expect a newborn to wake its mother after midnight 2.
We then add all the products in the 5 th column to get the variance of X. A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a hour shift. For a random sample of 50 patients, the following information was obtained.
What is the expected value? Suppose you play a game of chance in which five numbers are chosen from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A computer randomly selects five numbers from zero to nine with replacement. Over the long term, what is your expected profit of playing the game? To do this problem, set up a PDF table for the amount of money you can profit. That is the second column x in the PDF table below. To win, you must get all five numbers correct, in order.
The probability of choosing the correct first number is 1 10 1 10 because there are 10 numbers from zero to nine and only one of them is correct. The probability of choosing the correct second number is also 1 10 1 10 because the selection is done with replacement and there are still 10 numbers from zero to nine for you to choose. Due to the same reason, the probability of choosing the correct third number, the correct fourth number, and the correct fifth number are also 1 10 1 The selection of one number does not affect the selection of another number.
That means the five selections are independent. The probability of choosing all five correct numbers and in order is equal to the product of the probabilities of choosing each number correctly. Therefore, the probability of winning is. That is how we get the third column P x in the PDF table below. To get the fourth column x P x in the table, we simply multiply the value x with the corresponding probability P x.
Since —. You are playing a game of chance in which four cards are drawn from a standard deck of 52 cards. You guess the suit of each card before it is drawn. The cards are replaced in the deck on each draw. What is your expected profit of playing the game over the long term? Suppose you play a game with a biased coin. You play each game by tossing the coin once. If you play this game many times, will you come out ahead?
Do you come out ahead? Add the last column of the table. You lose, on average, about 67 cents each time you play the game, so you do not come out ahead. Suppose you play a game with a spinner. You play each game by spinning the spinner once.
If you land on blue, you don't pay or win anything. Complete the following expected value table:. Toss a fair, six-sided die twice. Construct a table like Table 4. Tossing one fair six-sided die twice has the same sample space as tossing two fair six-sided dice.
The sample space has 36 outcomes. Use this value to complete the fourth column. Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson. Most elementary courses do not cover the geometric, hypergeometric, and Poisson.
Your instructor will let you know if he or she wishes to cover these distributions. A probability distribution function is a pattern. You try to fit a probability problem into a pattern or distribution in order to perform the necessary calculations. These distributions are tools to make solving probability problems easier. Each distribution has its own special characteristics.
Learning the characteristics enables you to distinguish among the different distributions. Example 4. This table is called an expected value table. The table helps you calculate the expected value or long-term average. Try It 4. Define a random variable X. Solution 4. Print Share. Related Items Resources No Resources. Videos No videos. Documents No Documents. Links No Links.
Probability Formula: Probability formulas are useful for calculating the probability of an event to occur. Probability is the branch of Mathematics that deals with numerical descriptions of the chances of an event to occur. The probability of an event always lies between 0 and 1, where, 0 indicates an impossible event and 1 indicates a certain event. Suppose, the probability of occurrence of an event is x, then the probability that the event will not occur is denoted by 1-x. We use the basic probability formulas to determine the chances of an event happening. Though probability started with gambling, it is now used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc.
The binomial distribution is used to represent the number of events that occurs within n independent trials. Possible values are integers from zero to n. Where equals. In general, you can calculate k! If X has a standard normal distribution, X 2 has a chi-square distribution with one degree of freedom, allowing it to be a commonly used sampling distribution. The sum of n independent X 2 variables where X has a standard normal distribution has a chi-square distribution with n degrees of freedom. The shape of the chi-square distribution depends on the number of degrees of freedom.
Introduction to Statistics Worksheet 1. Save Image. Speech outline worksheet PDF. Item Preview. Tutorials Statistics and Probability. Calculus Tutorials and Problems. To print this worksheet: click the "printer" icon in toolbar below.
May 27, - The complete list of statistics & probability functions basic formulas cheat sheet for PDF download.
Considering the Probability and Statistics importance in exams like JEE Main, there are about questions that are asked directly from each chapter. So, you need to do thorough practice, you should try to solve different questions based on Probability and Statistics and make sure you are good with calculations. Generally, Statistics means fetching the values of some parameters and plotting or arranging them in a meaningful manner. Statistics is a procedure through which we can collect, analyze, interpret, present, and organize data.
It can be classified into various groups. Statistical data are the facts which are collected for the purpose of investigation. There are two types of statistical data:. As the primary data are collected by the user of the data, so it is more reliable and relevant. For example score of a cricket match noted from newspapers is secondary data.
Remember at the beginning of the chapter when we expressed our disdain for probability formulas? This activity will bring that idea full circle. Notice where formulas stand in our list of possible strategies to use for solving probability questions:. Sample Space. Venn Diagram.
We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in 2 to 5. Each face. One face has one dot, second face two dots, third face has three dots and … so on. We take them as 1, 2, 3, 4, 5, 6.
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