Exponential family expectations: Let p(y|φ) = c(φ)h(y) exp{φt(y)} be an exponential family model. a) Take derivatives with respect to φ of both sides of the equation R p(y|φ) dy = 1 to show that E[t(Y )|φ] = −c 0 (φ)/c(φ). b) Let p(φ) ∝ c(φ) n0 e n0t0φ be the prior distribution for φ. Calculate dp(φ)/dφ and, using the fundamental theorem of calculus, discuss what must be true so that E[−c(φ)/c(φ)] = t0.

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

How many different triangles can be constructed with the angle measurements of 134° 10° and 36° ?

Afamily went out to dinner and their bill was $113.if they want to leave a 19% tip, how much should they leave.