![to calculate E[Y+4] and Var[3Y] for the given probability distribution.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777569983998-3804a2412b4a1fce.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright Prime — let's do this. The problem asks to calculate E[Y+4] and Var[3Y] for the given probability distribution. First, let's verify the sum of probabilities: P(Y=0) + P(Y=1) + P(Y=2) + P(Y=3) + P(Y=4) = (1)/(8) + (19)/(84) + (1)/(6) + (5)/(168) + (7)/(24) To sum these, we find the least common multiple (LCM) of the denominators (8, 84, 6, 168, 2