Review statement of Problem 4.
Numerical examples:
\(\mathrm{1)}\ \ p = q = \dfrac{1}{2},\ l=1,\ m=2\).
\[ \begin{align} (L) &= p(1+q) = 2pq\left(1+ \dfrac{1}{2}\dfrac{p}{q}\right) = \dfrac{3}{4}, \\
(M) &= q^2 = \dfrac{1}{4}. \end{align} \]
\(\mathrm{2)}\ \ p=\dfrac{2}{5},\ q= \dfrac{3}{5},\ l=2,\ m=3\).
\[ \begin{align} (L) &= p^2\left\lbrace 1+ 2q + 3q^2\right\rbrace = 6p^2q^2\left\lbrace1 + \dfrac{2}{3}\dfrac{p}{q} + \dfrac{1}{6}\dfrac{p^2}{q^2}\right\rbrace = \dfrac{328}{625}. \\ (M) &= q^3 \left\lbrace 1+ 3p \right\rbrace = 4q^3 p\left\lbrace 1 + \dfrac{1}{4}\dfrac{q}{p}\right\rbrace = \dfrac{297}{625}. \end{align} \]
Continue to Markov's statement of Problem 8.