assignment you turn in needs to be your own work. 1. Suppose . That is‚ X has a normal distribution with μ=30 and σ2=144. 1a. Find a transformation of that will give it a mean of zero and a variance of one (ie.‚ standardize ). 1b. Find the probability that . 1c. Supposing 5X‚ find the mean of . 1d. Find the variance of . 2. A bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. The bank prides itself on its mortgage application
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to a camp. If 15% of the children in the school are first graders‚ and the 18 children are selected at random from among all 6 grades at the school‚ find the mean and variance of the number of first graders chosen? The mean is 2.7‚ and the variance is 2.3. n = 18 p = .15 q = .85 Mean = np = 18 x .15 = 2.7 Variance = npq = (18 x .15 x .85) = 2.295 ≈ 2.3 3. A producer plans an outdoor regatta for May 3. The cost of the regatta is $8000‚ which includes advertising‚ security‚ printing
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level‚ then we can conclude that we are 95% certain that there is no significant difference between the two population means. false 5. When comparing two population means based on independent random samples‚ the pooled estimate is used if the variances are unknown and assumed equal. true Chapter 12 6. The chi-square distribution is a continuous probability distribution that is symmetrical. false 7. In a contingency table‚ when all the expected frequencies equal the observed frequencies the calculated
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has the mean vector and variancecovariance matrix given below: Asset Mean VarianceCovariance Matrix 1 2 3 0.06 0.12 0.03 1 0.3 0.3 0.3 1 0.3 0.3 0.3 1 Weights Ones Mean Portfolio Return 1 1 1 0.176666122 Portfolio Portfolio Portfolio Variance STD Constraint 2.42961 1.558721 1 0.079372 1.603166 -0.68254 To model the portfolio choice problem‚ I begin by highlighting the mean vector and giving it a name. To do this‚ left-click on cell c9 and drag down until cell c11 and then release
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)2 / N ] * Population variance = σ2 = Σ ( Xi - μ )2 / N * Variance of 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 / (
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Source: Frerichs‚ R.R. Rapid Surveys (unpublished)‚ © 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling‚ but few use this method for population-based surveys. Rapid surveys are no exception‚ since they too use a more complex sampling scheme. So why should we be concerned with simple random sampling? The main reason is to learn the theory of sampling. Simple random sampling is the basic selection process of sampling and is
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0.30 E(R) 8.5% Covariance 0.014177 15.68% 11.91% 0.0153 Corr. 0.0246 9.76% S.D. 10.25% 0.009525 Variance 12% 0.99 EQ 7.2 Expected Return: E(RA) = (0.3) (‐0.05) + (0.4) (0.10) + (0.3) (0.20) = 0.085 = 8.5% E(RB) = (0.3) (‐0.10) + (0.4) (0.15) + (0.3) (0.30) = 0.12 = 12% EQ 7.3 Variance of Return: Var(RA) = (0.3) (‐0.05 – 0.085)2 + (0.4) (0.10 – 0.085)2 + (0.3)(0.20 – 0.085)2 = 0.009525 SD(RA) = Var(RA) ½ = (0.009525) ½ = 0
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Quantitative methods Time value of money Effective annual rate (EAR) Effective annual rate (EAR) = (1+stated annual rate/frequency‚ m) ^ m-1 Annuities Ordinary annuities: cash flow at the end of each period‚ normal one; Annuities due: cash flow at the beginning of each period‚ first payment =t0; Calculator setting: [2nd][BGN]-[2ND][SET]; same procedure for setback to END; Payment at beginning of next three years‚ N=4‚ always +1 using annuities due It is a BGN question‚ if first payment is today
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Time usually goes on the horizontal axis. B) Bar height or length should be proportional to the quantity displayed. C) Label data values at the top of each bar unless graphing lots of data. D) The non-zero origin rule may be waived for financial reports. Answer: D2. The ______________can be used to differentiate the "vital few" causes of quality problems from the "trivial many" causes of quality problems. A) histogramB) scatter plotC) Pareto chartD) box plotAnswer: C3. When using a dot plot to
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sample mean and variance of monthly 2 returns of a risky asset. Denote µa and σa the annualized sample mean and variance of returns of the risky asset. Then 2 (a). µa = 0.01 and σa = 0.024; 2 (b). µa = 0.12 and σa = 0.024; 2 (c). µa = 0.12 and σa = 0.288; (d). µa = 0.12 and σa = 0.024; (e). None of the above. 2. Which of the following statements is correct? (a). Expected utility of wealth is constant on the MVS. (b). In the standard deviation and expected return space‚ the mean-variance combination
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