clearly any outliers. (7) Jan 2001 2) The random variable X is normally distributed with mean 177.0 and standard deviation 6.4. (a) Find P(166 < X < 185). (4) It is suggested that X might be a suitable random variable to model the height‚ in cm‚ of adult males. (b) Give two reasons why this is a sensible suggestion. (2) (c) Explain
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means using random numbers in scientific computing. More precisely‚ it means using random numbers as a tool to compute something that is not random. For example1 ‚ let X be a random variable and write its expected value as A = E[X]. If we can generate X1 ‚ . . . ‚ Xn ‚ n independent random variables with the same distribution‚ then we can make the approximation A ≈ An = 1 n n Xk . k=1 The strong law of large numbers states that An → A as n → ∞. The Xk and An are random and (depending
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of Machine Learning Research‚ 5:448–455‚ 2009. 15. Li. Wan‚ Matthew. Zeiler‚ Sixin. Zhang‚ Yann. LeCun‚ and Rob. Fergus. Regularization of neural networks using dropconnect. ICML‚ 2013. 16. P. M. Wood. Universality and the circular law for sparse random matrices. The Annals of Applied Probability‚ 22(3):1266–1300‚ 2012.
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Random number tables have been used in statistics for tasks such as selected random samples. This was much more effective than manually selecting the random samples (with dice‚ cards‚ etc.). Nowadays‚ tables of random numbers have been replaced by computational random number generators. Tables of random numbers have the desired properties no matter how chosen from the table: by row‚ column‚ diagonal or irregularly. The first such table was published by a student of Karl Pearson’s in 1927‚ and
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exponential random variable with mean 5π cm. Each wire is cut to make rings of diameter 1 cm. Find the probability mass function for the number of complete rings produced by each length of wire. 4.85 The exam grades in a certain class have a Gaussian pdf with mean m and standard deviation σ. Find the constants a and b so that the random variable Y = aX + b has a Gaussian pdf with mean m and standard deviation σ . 4.86‚ 4.87 Let X = U n where n is a positive integer and U is a uniform random variable
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example‚ in PERT tasks are estimated with three numbers: The best case‚ the nominal case‚ and the worst case. These three estimates are combined into an expected duration‚ and a standard deviation. Thus the duration of each task is presumed to be a random variable with a known distribution. The math is very simple. Consider a task whose best/nominal/worst estimate is 3/5/9. The expected
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the fraction of the total number of items in several classes is a a. frequency distribution b. relative frequency distribution c. frequency d. cumulative frequency distribution 5. A tabular method that can be used to summarize the data on two variables simultaneously is called a. simultaneous equations b. crosstabulation c. a histogram d. an ogive Exhibit 1-1 A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they
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blood analysis from 1st procedure (x1‚x2) and 2nd procedure: (y1‚y2‚y3): * (x1‚y1)‚ x1‚y2‚x1‚y3 * x2‚y1‚x2‚y2‚x2‚y3 b. If the random variable of interest is the total number of steps required to do the complete analysis (both procedures)‚ show what value the random variable will assume for each of the experimental outcomes. Answer: Values for the random variable to be assumed for each of the outcomes. * (x1‚y1)=2 => the 1st procedure required 1 step and the 2nd procedure required 1 step
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be done by generating random numbers from given probability distributions. The different steps of this simulation and assumption made are explained below. 1. Simulation for the repair time. It is given that the repair time follows Repair Time (days) Probability 1. .20 2. .45 3. .25 4. .10 ----- 1.00 To generate a random number from the above
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Sampling Techniques Worksheet For each description of sampling‚ decide if the sampling technique is A. Simple Random B. Stratified C. Cluster D. Systematic E. Convenience 1. In order to estimate the percentage of defects in a recent manufacturing batch‚ a quality control manager at Intel selected every 8th chip that comes off the assembly line starting with the 3rd‚ until she obtains a sample of 140 chips. 2. In order to determine the average IQ of ninth-grade students‚ a school psychologist
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