\(\style{font-family:Times New Roman;}{\mu_{{\widehat p}_1-{\widehat p}_2}=P_1-P_2}\)
This means:
\(\style{font-family:Times New Roman;}{{\widehat p}_1-{\widehat p}_2}\)is the same thing as\(\style{font-family:Times New Roman;}{P_1-P_2}\).
\(\style{font-family:Times New Roman;}\mu\)is unbiased for\(\style{font-family:Times New Roman;}{P_1-P_2}\).
\(\style{font-family:Times New Roman;}{{\widehat p}_1-{\widehat p}_2}\)is unbiased for\(\style{font-family:Times New Roman;}{P_1-P_2}\).
\(\style{font-family:Times New Roman;}{P_1-P_2}\)is used to estimate\(\style{font-family:Times New Roman;}{{\widehat p}_1-{\widehat p}_2}\).