Assume that a RISC processor uses branch prediction to improve its performance. The following table gives the number of cycles taken for predicted and actual branch outcomes. These figures include both the cycles taken by the branch itself and the branch penalty associated with branch instructions.

If Pb is the probability that a particular instruction is a branch, p_t is the probability that a branch is taken, and P_w is the probability of a wrong prediction, derive an expression for the average number of cycles per instruction, T_ave· All non-branch instructions take one cycle to execute.  

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Prediction Not taken Taken Actual Not taken 1 2 Taken 4 1