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This means that over the long term of doing an experiment over and over, you would expect this average. You toss a coin and record the result. What is the probability that the result is he? If you flip a coin two times, does probability tell you that these flips will result in one he and one tail? You might toss a fair coin ten times and record nine he. Probability does not describe the short-term of an experiment. It 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 of each toss, obtaining he 12, times.
In his experiment, Pearson illustrated the Law of Large s. The Law of Large s states that, as the 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. In other words, after conducting many trials of an experiment, you would expect this average value.
The probability that they play zero days is 0. X takes on the values 0, 1, 2. In this column, you will multiply each x value by its probability. Expected Value Table. This table is called an expected value table. The table helps you calculate the expected value or long-term average. The expected value is 1. The 1. The fourth column of this table will provide the values you need to calculate the standard deviation. For each value x , multiply the square of its deviation by its probability. A hospital researcher is interested in the 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 s are chosen from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A computer randomly selects five s from zero to nine with replacement. Over the long term, what is your expected profit of playing the game? The values of x are not 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
To win, you must get all five s correct, in order. You may choose a more than once. The probability of choosing all five s correctly and in order is. Therefore, the probability of winning is 0. Since —0. 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. Suppose you play a game with a spinner. You play each game by spinning the spinner once. Like data, probability distributions have standard deviations. 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:. On May 11, at PM, the probability that moderate seismic activity one moderate earthquake would occur in the next 48 hours in Iran was about Suppose you make a bet that a moderate earthquake will occur in Iran during this period.
If you bet many times, will you come out ahead? Explain your answer in a complete sentence using s. What is the standard deviation of X? Hint: Construct a table to help you answer these questions. On May 11, at PM, the probability that moderate seismic activity one moderate earthquake would occur in the next 48 hours in Japan was about 1. As in Example 6, you bet that a moderate earthquake will occur in Japan during this period.
Find the mean and standard deviation of X. Some of the more common discrete probability functions are binomial , geometric , hypergeometric, and Poisson. Most elementary courses do not cover these distributions. 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. Class Catalogue at the Florida State University. The expected value, or mean, of a discrete random variable predicts the long-term of a statistical experiment that has been repeated many times. The standard deviation of a probability distribution is used to measure the variability of possible outcomes. Discrete Random Variables. Search for:. Calculate the standard deviation of the variable as well. Solution: You expect a newborn to wake its mother after midnight 2.
Try It You are playing a game of chance in which four cards are drawn from a standard deck of 52 cards. You lose, on average, about 67 cents each time you play the game so you do not come out ahead. Try It On May 11, at PM, the probability that moderate seismic activity one moderate earthquake would occur in the next 48 hours in Japan was about 1. s and Attributions.
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