random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is ‚ formally
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Probability distribution Definition with example: The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable‚ i.e. what is the possible number of times that head might occur? It is 0 (head never occurs)‚ 1 (head occurs once out of 2 tosses)
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The Poisson probability distribution‚ named after the French mathematician Siméon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson
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Probability Distribution Essay Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH‚ HT‚ TH‚ and TT. Now‚ let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0‚ 1‚ or 2‚ so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range‚ but are
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Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30‚000‚ [pic] [pic] Normal distribution [pic] [pic] 2. @ 15‚000 [pic] P(stockout) = 1 - .1635 = .8365 @ 18‚000 [pic] P(stockout) = 1 - .3483 = .6517 @ 24‚000 [pic] P(stockout) = 1 - .7823 = .2177 @ 28‚000 [pic]
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Statistics Chapter 5 Some Important Discrete Probability Distributions 5-1 Chapter Goals After completing this chapter‚ you should be able to: Interpret the mean and standard deviation for a discrete probability distribution Explain covariance and its application in finance Use the binomial probability distribution to find probabilities Describe when to apply the binomial distribution Use Poisson discrete probability distributions to find probabilities 5-2 Definitions Random Variables A
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Probability Distribution Memo To: Howard Gray‚ CEO; Jean Dubois‚ VP Mechanical Watch Division; Uma Gardner‚ VP Production; Amanda Hamilton‚ VP Marketing After identifying the business problem of falling sales and an increase in rejections by the Swiss Official Chronometer Control‚ conducting a study for research will prove to identify a solution. Researchers performed a study of a sample population of 500 people. The study reveals 60% of the watches purchased are certified and the average
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new Household appliance to potential customers. She has found from her years of experience that after demonstration‚ the probability of purchase (long run average) is 0.30. To perform satisfactory on the job‚ the salesperson needs at least four orders this week. If she performs 15 demonstrations this week‚ what is the probability of her being satisfactory? What is the probability of between 4 and 8 (inclusive) orders? Solution p=0.30 q=0.70 n=15 k=4 [pic] Using Megastat we get
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Discrete and Continuous Probability All probability distributions can be categorized as discrete probability distributions or as continuous probability distributions (stattrek.com). A random variable is represented by “x” and it is the result of the discrete or continuous probability. A discrete probability is a random variable that can either be a finite or infinite of countable numbers. For example‚ the number of people who are online at the same time taking a statistics class at CTU on
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22% said they watch the same amount and 8% said they watch more. Find the probability out of a randomly selected group of five that exactly three will say they watch less T.V. this year than last. a. Not binomial. b. N/A c. n=5 p=0.70 q=0.30 r: (0‚ 3.5) 2. There are 20 m&m’s candies in a dish. 8 are brown‚ three red‚ five green and four yellow. Two candies are picked from the dish at random. What is the probability that both are red? a. Binomial b. P(Success) = 6/20 = 3/10 P(Failure)
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