Random Pixel Poking

MATL, 15 14 13 bytes

8tE2$r&S1=3YG

Example (with MATL compiler running on MATLAB):

Or try it at MATL Online! (If it doesn't run the first time, press "Run" again or refresh the page). Note that the image is scaled by the online interpreter for better visualization.

This is a port of my Octave / MATLAB answer (see explanation there). Here are the equivalent statements:

MATL        Octave / MATLAB
----        ---------------
8tE         8,16
2$r         rand(...)
&S          [~,out]=sort(...)
1=          ...==1 
3YG         imshow(...)

Pyth - 16 15 bytes

Outputs image to o.png.

.wCm.S+255mZ7y8

Example image:

Processing, 74 73 bytes

fill(0);rect(0,0,15,7);stroke(-1);for(int i=0;i<16;)point(i++,random(8));

Sample output:

Explanation

fill(0);               //sets the fill colour to black
rect(0,0,15,7);        //draws a 16*8 black rectangle
stroke(-1);            //set stroke colour to white
for(int i=0;i<16;)     // for-loop with 16 iterations
 point(i++,random(8)); //  draw a point at x-coordinate i and a random y coordinate
                       //  the colour of the point is white since that is the stroke colour