Convolution

Prof. Richard B. Goldstein

There are two versions showing the convolution of

S = X₁ + X₂ + ... + X_k

where the X_i are identically distributed random variables.
If we set f(x) = Math.abs(x) with [a,b] = [-1,1] we get the following picture:

of X₁ alone. The following pictures show the sum for k =2, 3, and 4:

Options:

Single picture of pixel size 401 x 401 of the sum of k variables where k can range from 1 to 50.
All of the pictures of pixel size 201 x 201 from cases 2 to k where k can be up to 20.

There are two versions showing the convolution of
S = X₁ + X₂ + ... + X_k
where the X_i are identically distributed random variables. If we set f(x) = Math.abs(x) with [a,b] = [-1,1] we get the following picture:

of X₁ alone. The following pictures show the sum for k =2, 3, and 4:

Options: Single picture of pixel size 401 x 401 of the sum of k variables where k can range from 1 to 50. All of the pictures of pixel size 201 x 201 from cases 2 to k where k can be up to 20.

Note:	The pictures may be printed from Internet Explorer 5.5. They are not printable by Netscape 4.7. One solution is to use the "Print Screen" key to capture the picture on the clipboard and then use the Windows accessory package Paint or a similar package to cut the picture you want to save or print.