Answer:
[tex]D_m=1/2[/tex]
Explanation:
From the question we are told that
2 species
Assuming that questions a and be are solved
Diversity index D=2p_1p_2
with [tex]p_1 +p_2 =1[/tex]
Mathematically
[tex]D=2p_1(1-p_1)[/tex]
[tex]D=2(p_1-p_1^2)[/tex]
[tex]D=2({\frac{1}{4} -(p_1-1/2)^2}[/tex]
Therefore
[tex]D=\frac{1}{2} -2(p_1-1/2)^2[/tex]
Giving
[tex]D_m=1/2[/tex]
[tex]p_1=1/2[/tex]
