Suppose that random observations are needed from the triangular distribution whose probability density function is (a)Derive an expression for each random observation as a function of the uniform random number r.(b)Generate five random observations for this distribution by using the following uniform random numbers: 0.0956,0.5629,0.6695,0.7634,0.8426.(c)The inverse transformation method was applied to generate the following three random observations from this distribution: 0.09,0.64,0.49.Identify the three uniform random numbers that were used.d)Write an equation that Excel can use to generate each random observation from this distribution.

Question

Suppose that random observations are needed from the triangular distribution whose probability density function is  (a)Derive an expression for each random observation as a function of the uniform random number r.(b)Generate five random observations for this distribution by using the following uniform random numbers: 0.0956,0.5629,0.6695,0.7634,0.8426.(c)The inverse transformation method was applied to generate the following three random observations from this distribution: 0.09,0.64,0.49.Identify the three uniform random numbers that were used.d)Write an equation that Excel can use to generate each random observation from this distribution.

Quizplus · Accepted Answer

The Answer is (a)Applying the inverse transformation method,

(a)Applying the inverse transformation method, (b)Applying the formula obtained in part (a)yields the following random observations. (c)From part (a),we have r = x<sup>2</sup>,which yields the following uniform random numbers. (d)The equation that Excel can use is =SQRT(RAND()).

(b)Applying the formula obtained in part (a)yields the following random observations. (a)Applying the inverse transformation method, (b)Applying the formula obtained in part (a)yields the following random observations. (c)From part (a),we have r = x<sup>2</sup>,which yields the following uniform random numbers. (d)The equation that Excel can use is =SQRT(RAND()).

(c)From part (a),we have r = x²,which yields the following uniform random numbers. (a)Applying the inverse transformation method, (b)Applying the formula obtained in part (a)yields the following random observations. (c)From part (a),we have r = x<sup>2</sup>,which yields the following uniform random numbers. (d)The equation that Excel can use is =SQRT(RAND()).

(d)The equation that Excel can use is =SQRT(RAND()).

Suppose That Random Observations Are Needed from the Triangular Distribution