Templates and Macros: Macros: A macro can be stated as a string that compiler would replace with the defined value. Example: #define STRING "Value" Macros are not safe type, that is, float data is not accepted by a macro that is defined for integer operations. Type checking is not performed while expansion. Finding errors in macros is difficult. When a variable is post incremented or decremented, operation is been performed twice. Templates: A template is a way of making functions with independency in data type. Macros could not accomplish this task. Example: A sorting function does not bother the type of data it is sorting, since the applied algorithm is same. Syntax for Templates and Macros: The syntax for template definition is shown below Syntax for template: template <class type> type class-name<type>:: macro_name(arguments) { } The syntax for macro definition is shown below Syntax for macro: #define macro_name replacement-text return-type main() { Variable-name = macro_name(arguments); } Expansion is performed twice for the above macro. It denotes a limitation of macros. All occurrences of macro in file would be replaced by “replacement-text” before compilation of program. The template removes the macro limitations.

Question

using r language for integration theta = integral 0 to infinity (x^4)*e^(-x^2)/2 dx (1) use the density function of standard normal distribution N(0,1) f(x) = 1/sqrt(2pi) * e^(-x^2)/2 -infinity <x<infinity as importance function and obtain an estimate theta 1 for theta set m=100 for the estimate whatt is the estimate theta 1? (2)use the density function of gamma (r=5 λ=1/2)distribution f(x)=λ^r/Γ(r) x^(r-1)e^(-λx) x>=0 as importance function and obtain an estimate theta 2 for theta set m=1000 fir the estimate what is the estimate theta2? (3) use simulation (repeat 1000 times) to estimate the variance of the estimates theta1 and theta 2 which one has smaller variance?

Answer 1

Question

Chapter 1, Problem 7E

Program Plan Intro

Templates and Macros:

Macros:

A macro can be stated as a string that compiler would replace with the defined value.

Example: #define STRING "Value"

Macros are not safe type, that is, float data is not accepted by a macro that is defined for integer operations. Type checking is not performed while expansion.

Finding errors in macros is difficult.

When a variable is post incremented or decremented, operation is been performed twice.

Templates:

A template is a way of making functions with independency in data type. Macros could not accomplish this task.

Example: A sorting function does not bother the type of data it is sorting, since the applied algorithm is same.

Syntax for Templates and Macros:

The syntax for template definition is shown below

Syntax for template:

template <class type>

type class-name<type>:: macro_name(arguments)

{

}

The syntax for macro definition is shown below

Syntax for macro:

#define macro_name replacement-text

return-type main()

{

Variable-name = macro_name(arguments);

}

Expansion is performed twice for the above macro. It denotes a limitation of macros. All occurrences of macro in file would be replaced by “replacement-text” before compilation of program. The template removes the macro limitations.

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