Log/matrix/calc/algebra/probability/retarded question.

[morson]

Homework Statement

In the picture.

Homework Equations

The Attempt at a Solution

This is a really strange question. It's an extended-response exercise. I don't think it'd look pretty using the TeX thing, so I drew it in Paint. It combines all the topics we've done so far. Row 1 is easy. Row 2, column 1, I have no clue how to do. I'm not sure about the straight lines on the log in the bottom right, either.

http://img260.imageshack.us/img260/9584/blahgm8.png

 

[cristo]

In A₂₂, the vertical lines are absolute value signs, which basically means that you take the positive value of what's inside them. In general, these are needed since the logarithm function is only defined for postiive real numbers. However, in this case, the argument is positive, and they are not really needed.

For A₂₁, I'm afraid I don't really know what the Pr(A) and Pr(A') means. [Do you have the definition of Pr(A')? It looks like it must be equal to -Pr(A)]

 

[HallsofIvy]

Pr(A) and Pr(A'), I'm sure, are "Probabiliity that event A occurs" and "Probability even A does not occur". It's a bit annoying that they also use A to represent the entire matrix, but, hey, it's a silly exercise to begin with! Whatever "event A" is, Pr(A)+ Pr(A') is easy trivial!

Oh, and for A₂₂ use the obvious log_e e^x= x.

The problem I have is A₂₁:
\left(\frac{d}{dx}(x^2)\right)^0

I would interpret that as the derivative evaluated at x= 0 but then the answer is not what you give! The derivative evaluated at x= 1/2 will give that answer.

Finally, this is surely not "precalculus"!

 

[Hurkyl]

I'm pretty sure that's "raised to the 0-th power".

 

[HallsofIvy]

Ah, that makes sense!

 

[morson]

Ah, I see, so the probabilities added up is 1?

 

[HallsofIvy]

Yes, of course.