Consider the following modified version of the Sternberg memory-scanning paradigm. Each memory set always has four items. As always, presentation of the memory set is followed by a probe item. In this version of the paradigm, however, the probe item can occur multiple times in the memory set (whereas in the version we learned in class, the probe item could occur only once in each memory set). For example, in the following list, the probe item occurs three times:

Memory Set: T X T T
Probe Item: T

For convenience, let's call the number of times that the probe appears in the memory set the "probe size". In the example above, probe size is equal to 3. If the probe appeared just once in the memory set (as in the standard version of the paradigm), then probe size would equal 1, etc.

Derive the general predictions of the PARALLEL SELF-TERMINATING model for this version of the paradigm, assuming that each individual item comparison time is exponentially distributed. That is, determine how mean response time should vary as a function of probe size (1, 2, 3, and 4).

To derive the general predictions, first reason out the general process that governs this form of the paradigm. (For example, when we derived the predictions of the PARALLEL EXHAUSTIVE model for the regular version of the Sternberg paradigm, we reasoned out that the response time on each trial would be equal to the maximum of each of the individual comparison times. Use an analogous form of reasoning for the present model and paradigm.) Second, using the model that you derived from your reasoning, simulate 1000 trials of this paradigm for each probe size (1, 2, 3 and 4). These simulations will make use of the -cln(rand()) function that we used in lab. Finally, compute the average results of the simulations for each probe size. Explain intuitively why the predicted mean response times have the form that they do.