Suppose the strength of a particular metal beam is given by, S=10+.5T⋅P^2

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 T, P is has a normal distribution with mean T/2 and standard deviation T/12. For example E[P|T = 1] = 1/2, and

√V[P|T=1]=σ(P|T=1)=1/12
Required:
Compute the expectation of S.