  We compute effective bounds for $\alpha(n)$, the Fourier coefficients of
Ramunujan's mock theta function $f(q)$ utilizing a finite algebraic formula due
to Bruinier and Schwagenscheidt. We then use these bounds to prove two
conjectures of Hou and Jagadeesan on the convexity and maximal multiplicative
properties of the even and odd partition rank counting functions.
