I'm a bit stuck on this problem and need some help. The section we are covering is on Conditional expectation functions. You don't have to give me the full answer, but guide me through what I need to do to help me understand the concept.

Suppose the strength of a particular metal beam is given by, 5 = 5+272 . P Where T is a random variable representing the forging temperature and P is a random variable representing purity. Suppose the following statements are true about these random variables: . T has a uniform distribution on [0, 2). . Conditional on a value for 7, P is has a normal distribution with mean T/2 and standard deviation T/12. For example, if T = 1, then, E[PIT = 1] =5, and, [PIT = 1] = VV[PIT = 1] = 1 12 1. (6 points) Compute the expectation of S