> data=read.table("d:/111113/1.txt"‚header=T) > model1=lm(S~u_direction+mx+my+mz‚data) > summary(model1) Call: lm(formula = S ~ u_direction + mx + my + mz‚ data = data) Residuals: Min 1Q Median 3Q Max -11.8430 -0.3962 0.3252 0.7887 18.3963 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.50372 0.12738 -3.955 7.93e-05 *** u_direction -0.40368 0.07996 -5.048 4.85e-07 *** mx -0.40573 0
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Chapter 13: Chi-Square Applications SHORT ANSWER 1. When samples of size n are drawn from a normal population‚ the chi-square distribution is the sampling distribution of = ____________________‚ where s2 and are the sample and population variances‚ respectively. ANS: PTS: 1 OBJ: Section 13.2 2. Find the chi-square value for each of the right-tail areas below‚ given that the degrees of freedom are 7: A) 0.95 ____________________ B) 0.01 ____________________ C) 0.025 ____________________
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STA1101 Normal Distribution and Continuous random variables CONTINUOUS RANDOM VARIABLES A random variable whose values are not countable is called a _CONTINUOUS RANDOM VARIABLE._ THE NORMAL DISTRIBUTION The _NORMAL PROBABILITY DISTRIBUTION_ is given by a bell-shaped(symmetric) curve. THE STANDARD NORMAL DISTRIBUTION The normal distribution with and is called the _STANDARD NORMAL DISTRIBUTION._ Example 1: Find the area under the standard normal curve between z = 0 and z = 1.95 from z
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The Normal and Lognormal Distributions John Norstad j-norstad@northwestern.edu http://www.norstad.org February 2‚ 1999 Updated: November 3‚ 2011 Abstract The basic properties of the normal and lognormal distributions‚ with full proofs. We assume familiarity with elementary probability theory and with college-level calculus. 1 1 DEFINITIONS AND SUMMARY OF THE PROPOSITIONS 1 Definitions and Summary of the Propositions ∞ √ Proposition 1: −∞ 2 2 1 e−(x−µ) /2σ
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side of the centerline When the process is in statistical control‚ find the false alarm probability (Type-I error) for each case. The corresponding probability measures are obtained from the Normal table as P(3 " Z) = 0.00135 P(2 " Z) = 0.02275 P(1 " Z) = 0.1587 Solution: ! i) Use the Binomial distribution to ! calculate the probability measures. ! 3! 3! P(Y ! 2 n = 3‚ p = 0.02275) = (0.02275)2 (1" 0.02275) + (0.02275)3 = 0.00153 2!1! 3!0! Type-1 Risk considering both sides: ! = 0.00306
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Analysis for Managerial Applications Assignment No. : MS-08/TMA/SEM-I/2014 Coverage : All Blocks Note : Attempt all the questions and submit this assignment on or before 30th April‚ 2014 to the coordinator of your study center. 1. The distribution of Intelligence Quotient (I.Q.) scores measured for 100 students in a test is as follows: I.Q.* 40-50 50-60 60-70 70-80 80-90 90-100 Number of Students 10 20 20 15
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Variances Variances can be either: * Positive/favourable (better than expected) or * Adverse/unfavourable ( worse than expected) A favourable variance might mean that: * Costs were lower than expected in the budget‚ or * Revenue/profits were higher than expected By contrast‚ an adverse variance might arise because: * Costs were higher than expected * Revenue/profits were lower than expected What causes budget variance? There are four key reasons and it is important that
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AMA470 Midterm exam March 5‚ 2010 Please show full working out in order to obtain full marks. 1. Suppose that: • The number of claims per exposure period follows a Poisson distribution with mean λ = 110. • The size of each claim follows a lognormal distribution with parameters µ and σ 2 = 4. • The number of claims and claim sizes are independent. (a) Give two conditions for full credibility that can be completely determined by the information above. Make sure to define all terms in your definition
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April 2013. SPECIAL DISTRIBUTIONS I. Concept of probability (3%) 1. Explain why the distribution B(n‚p) can be approximated by Poisson distribution with parameter if n tends to infinity‚ p 0‚ and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with mean and standard deviation . 3. What is the relationship between exponential distribution and Poisson distribution? II. Computation
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Sampling distribution The sampling distribution is the distribution of the values of a sample statistic computed for each possible sample that could be drawn from the target population under a specified sampling plan. Because many different samples could be drawn from a population of elements‚ the sample statistics derived from any one sample will likely not equal the population parameters. As a result‚ the sampling distribution supplies an approximation of the true value’s population parameters
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