Following being diagnosed with brain cancer, how long is life expectancy?

Really depends. Are you talking a primary brain tumor or metastatic disease from another site. If a primary brain tumor, it depends on a few features - what grade - ie grade 2, 3, or 4, patient age, and other comorbidities. Grade 2s live about 10 years grade 3s live about 3-5 years grade 4s live if metastatic disease, survival is less than 1 year (if not shorter).