Investment Science Chapter 3 Dr. James A. Tzitzouris 3.1 Use A= 1− rP 1 (1+r)n with r = 7/12 = 0.58%‚ P = $25‚ 000‚ and n = 7 × 12 = 84‚ to obtain A = $377.32. 3.2 Observe that since the net present value of X is P ‚ the cash flow stream arrived at by cycling X is equivalent to one obtained by receiving payment of P every n + 1 periods (since k = 0‚ . . . ‚ n). Let d = 1/(1 + r). Then ∞ P∞ = P k=0 (dn+1 )k . Solving explicitly for the geometric series‚ we have that P∞ = Denoting
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that it produces is given by the function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum. Question: 1) Find the value of x. 2) In using regression analysis for making predictions what are the assumptions involved. 3) What is a simple linear regression model? 4) What is a scatter diagram method? CASE STUDY : 3 Mr Sehwag invests Rs 2000 every year with a company‚ which
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increases 3 points‚ the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information. e. none of these 3. If you are told a population has a mean of 25 and a variance of 0‚ what must you conclude? a. Someone has made a mistake. b. There is only one element in the population. c. There are no elements in the population. d. All the elements in the population are 25. e
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Covariance = 1/5 (-0.1-0.035)(0.21-0.04) + (0.2-0.035)(0.3-0.12) + (0.05-0.035)(0.07-0.12) + (-0.05-0.035)(-0.03-0.12) + (0.02-0.035)(-0.08-.012) + (0.09-0.035)(0.25-.012) = 0.00794 Variance of A = 1/5 (-0.1-0.035)2 + (0.2-0.08)2 + (0105 – 0.035)2 + (-0.05-0.035)2 + (0.02-0.035)2 + (0.09-0.035)2 = 0.01123 Variance of B = 1/5 (0.21-0.12)2 + (0.3-0.12)2 + (0.07-0.12)2 + (-0.03-0.12)2 (-0.08-0.12)2 + (0.25-0.12)2 = 0.02448 C. Correlation = 0.00794/(0.01123) (0.02448) = 0.479 12-4. Suppose all
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and an expected return of 3.5%‚ what kind of asset is it? Is it really risk-free? 5.Take the HMC management’s views of expected returns‚ standard deviation‚ and covariance of real returns as correct. Also‚ assume that cash is riskless (i.e. zero variance and covariance). If the board allows HMC to invest in only one asset class‚ which asset classes would you advise HMC to discard right away? Why? 6.If the board allows HMC to invest in assumed riskless cash and one other asset class‚ which asset
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areas totaling 42% The Second will be the size chart. This will measure tendency‚ variation‚ mean‚ median and mode. Descriptive Statistics: Size Mean 3.42 Standard Error 0.24593014 Median 3 Mode 2 Standard Deviation 1.73898868 Sample Variance 3.02408163 Kurtosis -0.7228086 Skewness 0.52789598 Range 6 Minimum 1 Maximum 7 Sum 171 Count 50 Frequency Distribution: Size Frequency 1 5 2 15 3 8 4 9 5 5 6 5 7 3 The mean household size of the customers is given as 3.42
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TUTORIAL 1 -95253936900 Each of the following processes involves sampling from a population. Define the population‚ and state whether it is tangible or conceptual. A shipment of bolts is received from a vendor. To check whether the shipment is acceptable with regard to shear strength‚ an engineer reaches into the container and selects 10 bolts‚ one by one to test. The resistance of a certain resistor is measured 5 times with the same ohmmeter 8 welds are made with the same process‚ and the
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Extra Exercise: Estimation and Hypothesis Testing 1. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information. 8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01 Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment. From a second large consignment‚ another 16 screws are selected at random and their mean and standard deviation found to be
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FALSE For a random variable X‚ let µ = E (X). The variance of X can be expressed as: V ar(X) = E X 2 − µ2 7. TRUE For random variables Y and X‚ the variance of Y conditional on X = x is given by: V ar(Y |X = x) = E Y 2 |x − [E (Y |x)]2 8. TRUE An estimator‚ W ‚ of θ is an unbiased estimator if E (W ) = θ for all possible values of θ. 9. FALSE The central limit theorem states that the average from a random sample for any population (with finite variance) when it is standardized‚ by subtracting the mean
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exponential probability density function. If then the cumulative distribution function of the exponential distribution is The following is the plot of the exponential cumulative distribution function. Mean and variance of an exponential function The mean and variance of an exponential function are respectively 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
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