Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), .

a. Graph the Gaussian for a =0.5, 1, and 2.

b. Given that , compute the area under the curves in part (a).

c. Complete the square to evaluate , where a > 0, b, and c are real numbers.

Problem 75E

Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), .

a. Graph the Gaussian for a =0.5, 1, and 2.

b. Given that , compute the area under the curves in part (a).

c. Complete the square to evaluate , where a > 0, b, and c are real numbers.

Answer;

Step-1;

Given gaussian function is; f(x) = .

Now , we have to sketch the graph the Gaussian for a = 0.5, 1, and 2.

If a = 0.5 , then the graph of the Gaussian function y= is;

If a = 1 , then the graph of the Gaussian function y= is ;

If a = 2 , then the graph of the Gaussian function y= is ;

Step-2;

b) Given that dx =

Now , we have to find out the area under the curves in part (a).

We know that dx = means area under the curve between , and x -axis is .

Therefore, the area under the curve between , and x -axis is;

dx = .Since a = 0.5

Thus , the area under the curve between , and x -axis is;

dx = .Since a = 1

Therefore , the area under the curve between , and x -axis is;

dx =