Statistics - Statistics is the science of collecting organizing‚ presenting‚ analyzing and interpreting data. It turns Data into information through transformation. Population ! - Everyone in group ! ! - µ is the mean ! - σ is the standard deviation Sample! - Some/Portion of group ! -x is the mean!! -S is the standard deviation Measurement Scales Types of Data Categorical/Qualitative Categorical/Qualitative Nominal! -Data has category but no order Data that can only be in categories
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Summary Software reliability modeling has‚ surprisingly to many‚ been around since the early 1970s with the pioneering works of Jelinski and Moranda‚ Shooman‚ and Coutinho. The theory behind software reliability is presented‚ and some of the major models that have appeared in the literature from both historical and applications perspectives are described. Emerging techniques for software reliability research field are also included. The following four key components in software reliability theory
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1 of 11 ID: MST.CPD.UD.03.0010 William is a quality inspector for an appliance manufacturer and is currently testing an oven. The oven starts off at room temperature‚ which is 70 degrees Celsius. William turns the oven to 167 degrees. The temperature in the oven increases from 70 degrees to 167 degrees over the following 10 minutes at a constant rate‚ so that the temperature follows a uniform distribution over the interval between 70 degrees and 167 degrees. At a randomly chosen time during that
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population proportion = σP2 = PQ / n * Standardized score = Z = (X - μ) / σ * Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] } Statistics Unless otherwise noted‚ these formulas assume simple random sampling. * Sample mean = x = ( Σ xi ) / n * Sample standard deviation = s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ] * Sample variance = s2 = Σ ( xi - x )2 / ( n - 1 ) * Variance of sample proportion = sp2 = pq / (n - 1) * Pooled sample
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using counting principles Organization of Data for Analysis Connecting questions and the data needed to answer them Understanding data concepts Statistics Single-variable data Two-variable data Evaluating validity Probability Distributions Discrete random variables Modelling Continuous Data Continuous random variables Culminating Projects and Investigations A: Permutations‚ Combinations‚ Probabilities; B: Statistics; C: Probability Distributions Counting Stories Project Choosing
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and 6 men. Find the probability that the committee has a) 3 women and 2 men. a) 4 women and 1 men. b) 5 women. c) at least 3 women. 3. In a school‚ 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) at least 6 students have access to the internet. 4. The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation
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Term Random Variable Definition A variable that takes on different numerical values based on chance Term Discrete Random Variable Definition A random variable that can only assume a finite number of values or an infinite sequence of values such as 0‚1‚2‚3.... Term Continuous Random Variables Definition Random variables that can assume any vallue in an interval. Term Expected Value Definition The mean of a probability distribution. the average value when the experiment
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another box contains 2 blue and 5 red pens. A pen drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box? (only write down the expression) P(first|blue) = P(blue|first) * P(first)/P(blue) = [3/(3+2) ]* [(3+2)/(3+2+2+5)] / [(3+2)/(3+2+2+5)] 5. A random variable must be: (1) random‚ (2) variable (i.e. a number that is not fixed). So which of them are random variables? (cycle the letters) – Answers are c and d. (a) (b) (c) (d)
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Universitat de Valncia May 20‚ 2010 Problem 35 Random variable X : weekly ticket sales (units) of a museum. X ∼ N(1000‚ 180) Find the probability of weekly sales exceeding 850 tickets. Find the probability of the interval 1000 to 1200 Take 5 weeks at random. Find the probability of weekly sales not exceeding 850 tickets in more than two weeks Ticket price is 4.5 Euros. Define the distribution of weekly revenue Problem 35 (a) Random variable X : weekly ticket sales (units) of a museum. X
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….‚ xk) Where x1‚ x2‚ x2‚ ….‚ xk Independent variables Y dependent variable Descriptive Predictive Prescriptive Math. Model Estimates of ind. Variables have to be made to predict the dep. variable There is uncertainty in the ind. Variables‚ this model describes the outcome or behavior of a given operations Taking different values of ind. Variables prescribes best possible Value for dependent variable The Problem –solving Process
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