Which of the following countries was part of the former Empire and became an independent republic?

Finland is the correct answer because it was part of the Russian Empire before declaring independence in 1917. Following the Russian Revolution, Finland took the opportunity to establish itself as a sovereign nation. The country had a degree of autonomy throughout its time within the Empire, but it ultimately sought full independence as the Empire's power weakened.

Russia and Poland have different historical contexts concerning their independence. Russia was the core of the Empire and transitioned into the Soviet Union after the revolution, not an independent nation emerging from the Empire in the same way as Finland. Poland, while it has a history of partitions that involved the dissolution of its statehood, was not directly part of the Empire in the time frame relevant to this question, as it had been partitioned by Russia, Prussia, and Austria before the rise of the Empire.

Serbia, similarly, was not part of the Russian Empire but was influenced by the larger dynamics of the Empire and the Balkan region. Instead, Serbia was an independent principality that had already established its sovereignty prior to the emergence of the Empire. Thus, Finland is the only country listed that fits the criteria of being an independent republic that emerged from the former Russian Empire.