A beam of length $ is rigidly supported at both ends. Experience shows that whenever the beam is hit at a random point, it breaks at a position X units from the right end, where X/$ is a beta random...

A beam of length $ is rigidly supported at both ends. Experience shows that whenever the beam is hit at a random point, it breaks at a position X units from the right end, where X/$ is a beta random variable. If E(X) = 3$/7 and Var(X) = 3 ℓ
²/98, find P (ℓ /7 ℓ/3).