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## Homework Statement

## Homework Equations

## The Attempt at a Solution

Continuous Uniform MGF is [itex]M_{x}(z) = E(e^zx) = \frac{e^{zb} - e^{za}}{zb - za}[/itex]

[itex]\frac{d}{dz}M_{x}(z) = E(X)[/itex]

Using the Product Rule

[itex]\ U = e^{bz} - e^{az}[/itex]

[itex]\ V = (zb - za)^{-1}[/itex]

[itex]\ U' = be^{bz} - ae^{az}[/itex]

[itex]\ V' = -1(zb - za)^{-2}(b - a)[/itex]

[itex]\frac{dM}{dz} = UV' + VU'[/itex]

[itex]\frac{dM}{dz} = (e^{bz} - e^{az})(-1(zb - za)^{-2}(b - a)) + ((zb - za)^{-1})(be^{bz} - ae^{az})[/itex] evaluated at z = 1

[itex]\ (e^{b}-e^{a})(-1)(b - a)^{-2}(b - a) + (b - a)^{-1}(be^{b} - ae^{a})[/itex]

[itex]\frac{e^{a} - e^{b} + be^{b} - ae^{a} }{b - a}[/itex]

The answer is [itex]\frac{b + a}{2}[/itex]

I'd really appreciate it if someone could tell me where i'm going wrong. Thanks.