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

• morson

In the picture.

## 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 [Broken]

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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 postive, 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)]

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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 loge ex= 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"!

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

Ah, that makes sense!

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

Yes, of course.