A loss variable [math]L[/math] has a density function that is proportional to

[[math]] x^{\alpha -1}e^{-x/\theta}. [[/math]]

The parameters [math]\theta [/math] and [math]\alpha [/math] are random with the following joint distribution

	[math]\alpha = 1 [/math]	[math]\alpha = 2[/math]
[math]\theta = 500 [/math]	0.25	0.35
[math]\theta = 1000 [/math]	0.15	0.25

Determine the standard deviation of [math]L[/math] to the nearest integer.

1. 298
2. 1,088
3. 1,220
4. 1,279
5. 1,565