A message is transmitted over a channel where each bit is inverted independently with probability $1-p \in ]0,1[$. Blocks of $r$ bits are transmitted. $X$ denotes the number of inversions during the transmission of a block of $r$ bits, and $X$ follows the distribution determined in Q16. We consider $\alpha \in ]0,1[$ and the condition $$\mathbb{P}(X \geqslant 2) \leqslant 1 - \alpha. \tag{II.2}$$ Using Markov's inequality, prove that if $r \leqslant 2 \frac{1-\alpha}{1-p}$, then condition (II.2) is satisfied.
A message is transmitted over a channel where each bit is inverted independently with probability $1-p \in ]0,1[$. Blocks of $r$ bits are transmitted. $X$ denotes the number of inversions during the transmission of a block of $r$ bits, and $X$ follows the distribution determined in Q16. We consider $\alpha \in ]0,1[$ and the condition
$$\mathbb{P}(X \geqslant 2) \leqslant 1 - \alpha. \tag{II.2}$$
Using Markov's inequality, prove that if $r \leqslant 2 \frac{1-\alpha}{1-p}$, then condition (II.2) is satisfied.