GCE Edexcel GCE in Mathematics Mathematical Formulae and Statistical Tables For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations = Core Mathematics C1 – C4 Further Pure Mathematics FP1 – FP3 Mechanics M1 – M5 Statistics S1 – S4 For use from June 2009 This copy is the property of Edexcel. It is not to be removed from the examination room or marked in any way. = TABLE OF CONTENTS Page 4 Core Mathematics C1 4 4 Mensuration Arithmetic series
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population based on information contained in a sample Random sample – every sample of the same size in the population has the same chance of being selected 1 2 POPULATION MEAN AND SAMPLE MEAN Set of all possible values of a random variable X Parameters: population mean µ 2 population variance σ X Given a random variable X (e.g. IQ scores‚ weights of all students‚ salaries of all workers‚ outcomes from tossing a die) We consider a random sample of size n the sample containing n observations
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generated a column of random numbers‚ which will help me to determine the weeks between breakdowns. I used the equation in excel =Rand( ). Next‚ I generated a column to determine the weeks between breakdowns. I used the formula in excel =8*SQRT(r) and used the previous mentioned randomly generated numbers. Once I had the randomly generated weeks‚ I created a column for the cumulative weeks to reach around the 52-week mark. Step 2 Step 2 I generated another column of random numbers‚ again using
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Unit 3 Tutorial Exercise Set 3A Calculating Probabilities Solutions can be found on page 6 1. Over a long period of time‚ the queue length of customers at the teller section of a major bank was observed to have the following probability distribution; Number in queue Probability 0 0.1 1 0.2 2 0.2 3 0.3 4 or more 0.2 Find the probability of a. At most two people in the queue. b. No more than three people in the queue. c. At least one person in the queue. d. Two or
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Simulation * Discrete Probability Distribution * Confidence Intervals Calculations for a set of variables Mean Median 3.2 3.5 4.5 5.0 3.7 4.0 3.7 3.0 3.1 3.5 3.6 3.5 3.1 3.0 3.6 3.0 3.8 4.0 2.6 2.0 4.3 4.0 3.5 3.5 3.3 3.5 4.1 4.5 4.2 5.0 2.9 2.5 3.5 4.0 3.7 3.5 3.5 3.0 3.3 4.0 Calculating Descriptive Statistics Descriptive Statistics: Mean‚ Median Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Mean 20 0 3.560 0.106
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Example 28 If jobs arrive every 15 seconds on average‚ λ= 4 per minute‚ what is the probability of waiting less than or equal to 30 seconds‚ i.e .5 min Example 29 If ‚ find ‚ and Example 30 Refer to Example 26. The random variable has a pdf which is an exponential distribution. The Poisson Process Recall that the Poisson distribution is often used to model the number o f events that occur in a given region of time or space. We say that the events follow a Poisson
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Proposal – Generalizations of Newsvendor Problem 1. Introduction: The newsvendor model has been used in operations management and applied economics for years to determine optimal ordering quantity under uncertain demand. Perishable goods such as banana and lettuce cannot be carried from one period to another. Managers have to make decision on the inventory level of perishable goods over a very limited period. For example‚ due to the uncertainty of the demand of the newspaper‚ the newsboy
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Question 1 1. The manager of Queensland Health’s computer network constructed the probability distribution for the number of interruptions to the system per day using historical data: Interruptions per day | 0 | 1 | 2 | 3 | 4 or more | Probability | 0.39 | 0.31 | 0.1 | 0.09 | ? | Determine the probability that on a given day there are more than two interruptions to the system. (2 decimal places) 2 points Question 2 1. The mean and standard deviation of a binomial distribution
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Georgia Institute of Technology School of Electrical and Computer Engineering ECE6604 Personal & Mobile Communications Final Exam Spring 2010 Tuesday May 6‚ 11:30am - 2:20pm • Attempt all questions. • All questions are of equal value. • Open book‚ open notes‚ exam. 1a) 5 marks: The LCR at the normalized threshold ρ for a 2-D isotropic scattering channel can be expressed as √ 2 LR = 2πfm ρe−ρ ‚ where ρ= Δ and Rrms = R Ωp = R Rrms E[α2 ] is the rms envelope level
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example‚ the proportion of individuals in a random sample who support one of two political candidates fits this description. In this case‚ the statistic is thecount X of voters who support the candidate divided by the total number of individuals in the group n. This provides an estimate of the parameter p‚ the proportion of individuals who support the candidate in the entire population. The binomial distribution describes the behavior of a count variable X if the following conditions apply: 1: The
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