Computational Efficiency of Polar and Box Muller Method: Using Monte Carlo Application

As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.

A soccer ball manufacturer wants to estimate the mean circumference of mini-soccer balls within .12 inch.  Assume that the population of circumferences is normally distributed.

Statistical results of the data analysis have been received by using the Gauss curve, as preferred distribution function, and the

21. Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of .6. Both women’s and men’s reach from this position is normally distributed. If this design is implemented:

by the Trapezoidal rule is Etrap = O(h2 ) and by Simpson’s rule is ESimp = O(h4 ). i) For each of these numerical integration rules, what conditions are required on the integrand f so these error estimates are valid? ii) Suppose that the error using h = 5 × 10−3 is E0 = 1.19 × 10−4 when using either the Trapezoidal rule or Simpson’s rule. For both rules, ˆ estimate the error if an interval width of h = 1 × 10−3 is used. iii) The Matlab command [z, w] = gauleg(N); calculates the N Gauss-Legendre nodes z and weights w for the interval [−1, 1]. Show how z and w can be used to numerically calculate

M2 through M8 by the probability values calculated in column I, that is, formulas for

Using SQL and avoiding over complicating my code helped me to easily trace the code as mathematical equations was a big part of the assignment and each mean, variance (standard deviation) and normal distribution function had to be recalculated by hand to ensure that no logical or mathematical errors existed. Thus making my overall approach to the assignment much more

© The Authors JCSCR. (2012). A Comparative Study on the Performance. LACSC – Lebanese Association for Computational Sciences Registered under No. 957, 2011, Beirut, Lebanon, 1-12.

i) How does the shape of the distribution impact what you conclude? The shape distribution is out of range.

8. Review the following frequency distribution. Create a histogram either by hand or by using some other

Step One: Create a random right triangle with the legs the length of a and b, and hypotenuse the length of c.

σ_(R_X )=√(((∂R_X)/(∂V_1 ))^2 〖σ_(V_1 )〗^2+((∂R_X)/(∂V_2 ))^2 〖σ_(V_2 )〗^2+((∂R_X)/(∂I_D ))^2 〖σ_(I_D )〗^2+ ((∂R_X)/(∂R_S ))^2 〖σ_(R_S )〗^2 )

The best mean TTS reduction for the nine scenarios that can be obtained using ALINEA and PI-ALINEA are $10,3\%$ and $20,6\%$, respectively.

Step 2 Each step has a length of 10σ/N and identify the mid-point of each interval µ-4.9σ, µ-

1989). The difference betwe en the two approaches can be viewed in ter ms of