Project #63151 - monte carlo

1.Suppose you wish to select 3 numbers randomly from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Explain how you would do this. (You’re selecting three different numbers.)

 

2.

Suppose I execute the following code:

 

P[0] = 0; P[1] = .1; P[2] = .5; P[3] = .7; P[4] = .75; P[5] = 1;

 

X[1] = 3; X[2] = 5; X[3] = -1; X[4] = 10; X[5] = 20;

 

U = MTUinform (0);

 

for (i = 1; i <= 5; i++) {

 

if (U <= P[i]) {

 

Y = X[i];

 

break;

 

}

 

}

 

Here all the variables are integers except for U and the P array, which are a doubles. What is the probability mass function for the random variable Y?

3.Write code that does the same thing (as question 2) more efficiently

 

 

4.

Suppose I execute the following code:

 

a[1] = a[2] = a[3] = a[4] = .5; a[5] = 1;

 

accepted = 0;

 

while (!accepted) {

 

U = MTUniform (0); V = MTUniform (0);

 

Xtilde = 1 + (int) (5 * U);

 

if (V <= a[Xtilde]) {

 

X = Xtilde;

 

accepted = 1;

 

}

 

}

 

Here all the variables are integers except U, V, and the array, which are doubles. What is the probability mass function for the random variable X that is generated?

5.

Suppose we execute the following code:

 

U = MTUniform (0);

 

X = sqrt(U);

 

Here both U and X are doubles. What is the density function of X?

 

 

 

 

Subject Computer
Due By (Pacific Time) 03/22/2015 12:00 am
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