Concept explainers
VarianceReduction by Antithetic Variates. A simple and widely used technique for increasing the efficiency and accuracy of Monte Carlo simulations in certain situations with little additional increase in computational complexity is the method of antithetic variates. For each
Use the parameters specified in Problem
Equation
of
Equation
for the option price. Thus the Monte Carlo estimate
Use the difference equation
where
And
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardEconomics Now suppose that the time series process {Xt}, is expressed as Xt = z + et where et is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and et are uncorrelated: i. Find the mean xt , E(Xt) and the variance Xt, var(Xt). Do they depend on t? ii. Determine the covariance of xt and xt+h for h > 0, Cov(Xt , xt+h) iii. Is xt stationary? Explain.arrow_forwardIf X is a Poisson variable such that P(X = 2) = 9P(X = 4) +90 P(X = 6), find the mean and variance of X.arrow_forward
- If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.arrow_forwardA research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 31% say that they would travel into space on a commercial flight if they could afford it. At x = 0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. B. No more than % of adults in the country would travel into space on a commercial flight if they could afford it. C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not % of adults in the country would travel into space…arrow_forwardIf the moment-generating function of X is find (a) The mean of X. M(t) = exp(166t + 200t²), (b) The variance of X. - Find the distribution of W = X² when X is N(0,9), (c)Pr(170 < X < 200).arrow_forward
- DDT (dichlorodiphenyltrichloroethane) was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 200 kilograms of DDT that has seeped into the soil. t = time in yearssince application D = DDT remaining,kilograms 0 200.00 1 190.00 2 180.50 3 171.48 (a) Show that the data are exponential. The ratio from year 0 to year 1 is ______ , from year 1 to year 2 is ____ , and from year 2 to year 3 is_____ (rounded to two decimal places). Because these successive ratios are all , a) different b)the same , the data are exponential.arrow_forwardIn time-series decomposition, seasonal factors are calculated by Multiple Choice O O O O O SFt (Y) (CMA). SFt= Y/CMAt (CMA+) x (SFt) =Yt. SFt = Yt - CMAt. None of the options are correct.arrow_forwardNo, this solution is not correct. The variance of an exponentially distributed random variable is the square of its mean, so Var(L) = (1/Y)^2. However, the given solution incorrectly multiplies this by Var(Y) to obtain an incorrect expression for Var(L). The correct approach to find Var(L) involves using the law of total variance. The law of total variance states that Var(L) = E[Var(L|Y)] + Var(E[L|Y]). We already know that Var(L|Y) = (1/Y)^2, so E[Var(L|Y)] = E[(1/Y)^2]. We also know that E[L|Y] = 1/Y, so Var(E[L|Y]) = Var(1/Y). To find E[(1/Y)^2] and Var(1/Y), we need to use the formulas for the expected value and variance of a function of a random variable. These involve integrating the function multiplied by the probability density function of the random variable. Once we correctly compute E[(1/Y)^2] and Var(1/Y), we can plug the correct values into the law of total variance to find the correct value for Var(L).arrow_forward
- (10) For the above problem verify that the theorem of total variance (TTV) holds. The following verifications are proposed. (a) Since Var(Var(X|Y)) = o = Var(X), the TTV holds. (b) Since poVar(Y) Var(E(X|Y)) + E(Var(X|Y)) = +ož(1– p²) = o = Var(X). the TTV holds. (c) Since Var(E(X|Y)) = Var(X) = o3, the TTV holds. (d) Since Var(E(x|Y)) = 0 and E(Var(X|Y)) = Var(X), the TTV holds. (e) None of the above The correct verification is (a) (b) (c) (e) N/A (Select One)arrow_forward(x - x)? y-y (x- x)(y- y) 6. 1 2 3 3 1 4 Ex; Ey = {(x; - x) E(x; – x)² = E(y; - y) E(x; - x)(y - y) = %3D %3D (a) Complete the entries in the table. Put the sums in the last row. What are the sample means and y? (b) Calculate bị and b, using (2.7) and (2.8) and state their interpretation. (c) Compute E} x}, £?-1x;yi. Using these numerical values, show that E(x; – x) = Ex} – Nx and E(x - x)(y; - ) = Exy - Nxy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. yi 6. 2 2 3 3 1 4 Ex; = Ey = %3D %3D %3D (e) On graph paper, plot the data points and sketch the fitted regression line ŷ = b + b2x. (f) On the sketch in part (e), locate the point of the means (x, y). Does your fitted line pass through that point? If not, go back to the drawing board, literally. (g) Show that for these numerical values y= b + b,x. (h) Show that for these numerical values y = y, where y = Eỳi/N. (i)…arrow_forwardExample 17: If P (x) = 0.1 x ,x= 1, 2, 3, 4 = 0 %3D *, otherwise find (i) P{X=1 or 2 } (ii) Parrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning