the median (2 marks) c) If on Saturday she spent RM8‚ what is the median for these six days? (2 marks) d) Make a sketch of the data‚ showing the mean and median values. Comment on it. (4 marks) 5) Differentiate between discrete random variable and continuous random variable. Give an example for each of this category. (6 marks) 6) Differentiate descriptive statistics and inferential statistics using an example. (5 marks) WOU University has nearly 300 students. In a recent study done on 30 students
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value. Show that this trend is positive. Estimate the level of pollution at noon on a day when the temperature and humidity index is 75. (Note that over the 10 days‚ the temperature and humidity index ranged from 30 to 95) (15 marks) 2. A random variable X N ( ‚ 2 ) (a) If 30 ‚ 2 16 ‚ find the probability of P(X < 33) . (b) If 25 ‚ 2 9 ‚ find the value of k for P(X > k) = 0.0537 (15 marks) 3. The length of rods in a large batch with mean 120 mm and a standard deviation
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start this question we must understand what chance is. In a dictionary‚ chance is defined as the possibility of something happening or not happening. With chance we often also describe events that are unpredictable‚ in other words‚ random. We can define something is random by knowing that the chance of a particular event happening is not effected by anything. Knowing this‚ what events that have importance in our modern day society have been caused by chance or randomness? Can we claim that chance
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Definitions Random Variables A random variable represents a possible numerical value from an uncertain event. Discrete random variables produce outcomes that come from a counting process (e.g. number of classes you are taking). Continuous random variables produce outcomes that come from a measurement (e.g. your annual salary‚ or your weight). Chap 5-3 Copyright ©2012 Pearson Education‚ Inc. publishing as Prentice Hall Definitions Random Variables Random Variables Ch. 5 Discrete
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Chapter 3: Survival Distributions and Life Tables Distribution function of X: Force of mortality µ(x): fX (x) 1 − FX (x) s (x) = − s(x) FX (x) = Pr(X ≤ x) µ(x) = Survival function s(x): s(x) = 1 − FX (x) Relations between survival functions and force of mortality: x Probability of death between age x and age y: Pr(x < X ≤ z) = FX (z) − FX (x) s(x) = exp − = s(x) − s(z) Pr(x < X ≤ z|X > x) = = µ(y)dy x FX (z) − FX (x) 1 − FX (x) s(x) − s(z) s(x) Derivatives: d t qx dt d t px
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the probability that less than one month elapses between accidents. (e) If no accidents have occurred within the last six months‚ what is the probability that an accident will occur within the next year? Question 4: [20 points] If T is a continuous random
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uncertainty exists in model parameters. 2. A continuous random variable may assume only integer values within a given interval. 3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously. 4. A decision tree is a diagram consisting of circles decision nodes‚ square probability nodes‚ and branches 5. Starting conditions have no impact on the validity of a simulation model. 6. A table of random numbers must be normally distributed and efficiently
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Relative frequency of a category = Frequency of that category Sum of all frequencies Class width = Upper boundary– Lower boundary Class midpoint or mark = Lower limit+ Upper limit/2 Approximate class width=Largest value -mallest value / Number of classes Relative frequency of a class=Frequency of that class/Sum of all frequencies Cumulative relative frequency=Cumulative frequency of a class/Total observations in the data set Mean = Average ‚ Median ‚ Mode Range = Largest value–
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200 IEEE TRANSACTIONS ON SYSTEMS SCIENCE AND CY13ERNETICS‚ VOL. A Tutorial Introduction SSC-4‚ NO. 3‚ SEPTEMLIER 1968 to Decision Theory D. WARNER NORTH Abstract-Decision theory provides a rational framework for choosing between alternative courses of action when the consequences resulting from this choice are imperfectly known. Two streams of thought serve as the foundations: utility theory and the inductive use of probability theory. The intent of this paper is
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Chapters 1-3:In order to control costs‚ a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157‚ $132‚ $109‚ $145‚ $125‚ $139. Calculate the mean and sample variance(s^2) and standard deviation. Mean = 807/6 = 134.5. Sample Variance = (109925 – (807^2/6)/6-1 = (109925 – 108541)/5 = 1384/5 = 276.8.
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