Question: There are two drivers. Driver A has the loss distribution X with E[X] = 4 and Std[X] = 6. Driver B has the loss distribution

There are two drivers. Driver A has the loss distribution X with E[X] = 4 and Std[X] = 6. Driver B has the loss distribution Y with E[Y] = 6 and Std[Y] = 5. A & B want to share the risk by pooling their risks. Let Z be the loss distribution of each driver (i.e. average). If additionally Corr[X,Y] = 0.05 is known, what is the standard deviation of Z?

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