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Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
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∙ 14y ago
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
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∙ 14y ago
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What is the meaning of expected value in a probability distribution?
The expected value is the average of a probability distribution. It is the value that can be expected to occur on the average, in the long run.
What is The mean of a discrete probability distribution is also called the?
The mean of a discrete probability distribution is also called the Expected Value.
Real world examples of binomial distribution?
This is interactive mathematicswhere you learn math by playing with it!homesitemapLiveMath infoFlash highlightsScientific Notebookmath blogaboutfeedback12. The Binomial Probability DistributionA binomial experiment is one that possesses the following properties:On this page...Mean and variance of a binomial distributionThe experiment consists of n repeated trials;Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial);The probability of a success, denoted by p, remains constant from trial to trial and repeated trials are independent.The number of successes X in n trials of a binomial experiment is called a binomial random variable.The probability distribution of the random variable X is called a binomial distribution, and is given by the formula:P(X) = Cnxpxqn−xwheren = the number of trialsx = 0, 1, 2, ... np = the probability of success in a single trialq = the probability of failure in a single trial(i.e. q = 1 − p)Cnx is a combinationP(X) gives the probability of successes in n binomial trials.Mean and Variance of Binomial DistributionIf p is the probability of success and q is the probability of failure in a binomial trial, then the expected number of successes in n trials (i.e. the mean value of the binomial distribution) isE(X) = μ = npThe variance of the binomial distribution isV(X) = σ2 = npqNote: In a binomial distribution, only 2 parameters, namely n and p, are needed to determine the probability.EXAMPLE 1Image sourceA die is tossed 3 times. What is the probability of(a) No fives turning up?(b) 1 five?(c) 3 fives?AnswerLoading...EXAMPLE 2Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?AnswerLoading...EXAMPLE 3Image sourceIn the old days, there was a probability of 0.8 of success in any attempt to make a telephone call.Calculate the probability of having 7 successes in 10 attempts.AnswerLoading...EXAMPLE 4A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of(a) more than 2 hits?(b) at least 3 misses?AnswerLoading...EXAMPLE 5Image sourceThe ratio of boys to girls at birth in Singapore is quite high at 1.09:1.What proportion of Singapore families with exactly 6 children will have at least 3 boys? (Ignore the probability of multiple births.)[Interesting and disturbing trivia: In most countries the ratio of boys to girls is about 1.04:1, but in China it is 1.15:1.]AnswerLoading...EXAMPLE 6A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain(a) no more than 2 rejects? (b) at least 2 rejects?AnswerLoading...11. Probability Distributions - Concepts13. Poisson Probability DistributionDidn't find what you are looking for on this page? Try search:The IntMath NewsletterSign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!Given name: * requiredFamily name:email: * requiredSee the Interactive Mathematics spam guarantee.Probability Lessons on DVDEasy to understand probability lessons on DVD. See samples before you commit.More info: Probability videosBookmark this pageAdd this page to diigo, Redditt, etc.Need a break? Play a math game. Well, they all involve math... No, really!Help keep Interactive Mathematics free!Home | Sitemap | About & Contact | Feedback & questions | Privacy | IntMath feed |Hello, PakistanPage last modified: 22 March 2007Valid HTML 4.01 | Valid CSSChapter ContentsCounting and Probability - Introduction1. Factorial Notation2. Basic Principles of Counting3. Permutations4. Combinations5. Introduction to Probability Theory6. Probability of an EventSingapore TOTOProbability and Poker7. Conditional Probability8. Independent and Dependent Events9. Mutually Exclusive Events10. Bayes' Theorem11. Probability Distributions - Concepts12. Binomial Probability Distributions13. Poisson Probability Distribution14. Normal Probability DistributionThe z-TableFollowing are the original SNB files (.tex or .rap) used in making this chapter. For more information, go to SNB info. SNB files1. Factorial Notation (SNB)2. Basic Principles of Counting (SNB)3. Permutations (SNB)4. Combinations (SNB)5. Introduction to Probability Theory (SNB)6. Probability of an Event (SNB)Singapore TOTO (SNB)Probability and Poker (SNB)7. Conditional Probability (SNB)8. Independent and Dependent Events (SNB)9. Mutually Exclusive Events (SNB)10. Bayes' Theorem (SNB)11. Probability Distributions - Concepts (SNB)12. Binomial Probability Distributions (SNB)13. Poisson Probability Distribution (SNB)14. Normal Probability Distribution (SNB)Comments, Questions?Math ApplicationsI get a good understanding of how math is applied to real world problems:In most lessonsIn some lessonsRarelyNeverVotes so far: 1570Follow IntMath on TwitterGet the Daily Math Tweet!IntMath on TwitterRecommendationEasy to understand probability lessons on DVD. Try before you commit. More info:MathTutorDVD.comFrom the math blog...Free math software downloadsWanting to use some math software but find it's too expensive? Here are some free math software downloads to consider....more »CrazyEgg Web AnalyticsCrazyEgg gives us a wealth of information about visitors to a Website - where they came from, how long they stay and where they go next....more »Algebrator reviewAlgebrator is an interesting product - but I'm not sure that I can recommend it....more »
Is the mean of probability distribution is called its expected value?
No. The mean is the expected value of the random variable but you can also have expected values of functions of the random variable. If you define X as the random variable representing the result of a single throw of a fair die, the expected value of X is 3.5, the mean of the probability distribution of X. However, you play a game where you pay someone a certain amount of money for each throw of the die and the other person pays you your "winnings" which depend on the outcome of the throw. The variable, "your winnings", will also have an expected value. As will your opponent's winnings.
How do you find the expected value of X?
For a discrete probability distribution, you add up x*P(x) over all possible values of x, where P(x) is the probability that the random variable X takes the value x. For a continuous distribution you need to integrate x*P(x) with respect to x.
What is the meaning of expected value in a probability distribution?
The expected value is the average of a probability distribution. It is the value that can be expected to occur on the average, in the long run.
Which expression is used to find the expected value of X in binomial distribution?
If X takes the value 1 with probability p and 0 with probability (1-p), and there are n independent trials then E(X) = np
The expected value is what kind of aspect of how probability distribution is characterized?
Expected value is the outcome of confidence of how probability distribution is characterized. If the expected value is greater than the confidence interval then the results are significant.
What is The mean of a discrete probability distribution is also called the?
The mean of a discrete probability distribution is also called the Expected Value.
An experiment is conducted in which two fair coins are tossed and the number of heads is recorded. The binomial random variable, X, is the number of heads?
thas so true
What does the expected value of a binomial distribution with n trials tell you?
average number of successes
What is the expected value of this distribution if the probability of success on a single trail is 0.5?
This is the answer.
Can the expected value of a discrete probability distribution be negative?
Yes it can be negative.
What is symmetric distribution?
It is a probability distribution in which the probability of the random variable being in any interval on one side of the mean (expected value) is the same as for the equivalent interval on the other side of the mean.
What shows the skewness of a probability distribution?
The third moment. That is, the expected value of the cubes of the deviations from the mean.
Another name for the mean of a probability distribution is its expected value true or false?
Yes, it is true.
What is Hypothesis Testing of Goodness-of-Fit?
A test using relative errors comparing a frequency table to the expected counts determined using a given probability distribution; the null hypothesis is that the given probability distribution fits the data's distribution.
