Assume a female and male monkey.
Lets call this generation $1$.
All males and females have one and one only partner for breeding in their entire life assuming there is at least $1$ available.
And they only breed with others of their own generation.
All females give birth to all their boys (if any) before all their girls(if any).
All females and males live for $1$ generation and they never try to kill eachother nor have enemies and there is sufficient food.
The probability for birth of a boy is independant of that for a girl and vice versa.
Males do not get pregnant.
All Females that find a Male get pregnant in their lifetime but not all give succesful birth.
Lets denote the probability for birth from a female -that finds a male - in her entire lifespan by $P(x)$.
$P(0$ $ sons) = X$
$P(1$ $ son) = A$
$P(2$ $ sons) = B$
$P(3$ $ sons) = C$
$P(4$ $ sons) = D$
note again that the probability of birth for boys and girls is unrelated !
Thus $X+A+B+C+D = 1$
For daughters we have
$P(0$ $ daughters) = Y$
$P(1$ $ daughter) = A^*$
$P(2$ $ daughters) = B^*$
$P(3$ $ daughthers) = C^*$
( And here also $Y+A^*+B^*+C^*=1$ ofcourse )
(Note that there is no change per generation for the birth probabilities per pregnant(!) female.)
Let generation be $G$, the amount of sons of $G$ be $M$ and the amount of daughters of $G$ be $F$.
Let $P_M(G,X,A,B,C,D,Y,A^*,B^*,C^*)$ be the probability for $M$ sons in generation $G$ with the given birth probabilities.
Let $P_F(G,X,A,B,C,D,Y,A^*,B^*,C^*)$ be the probability for $F$ daughters in generation $G$ with the given birth probabilities.
Let $exp(G,X,A,B,C,D,Y,A^*,B^*,C^*)$ be the expectation value for children in generation $G$.
Find expressions for $'P_M'$ , $'P_F'$ and $'exp'$.