Week 2 Flashcards
What does the first derivative of a curve give?
The slope of a tangent at that point.
What is a good rule of thumb for investing in stocks vs bonds?
Take 100 and subtract your age, be invested in that amount of stocks and the rest in bonds.
What does numerical calculus involve?
Instead of doing analytical calculus to calculate the derivative of the equation, just use the equation and take very small steps, the smaller the step the closer to the analytical value.
what is the derivative of e^x? What about ln(x)
e^x, ln(x) is 1/x.
What must we balance against returns?
Our expected risk.
What does solving an integral give?
The area under a curve.
How do we get the mean value of adataset given probabilities and associated values?
It will be given by the sum of each probability * the associated possible value.
What do the parts of (E(X) = integral of x fx(x) dx) mean?
Fx(x) is the height of the distribution curve. Dx is the width, in a distribution curve width * height gives probability. This makes fx(x) probability density and fx(x) * dx a probability. The integral sign is a stretched out S, for sum. So E(X) is the sum of x values * its probability.
What is a convergent integral?
One that as more steps are done the value converges to a single value.
How many rows and columns does a 3*7 matrix have? Where would I find matrix entry a2,4
3 rows, 7 columns.
You would find a2,4 in the 2nd row, and 4th column.
What does it mean for a variable to be distributed normally?
A normally distributed variable will be randomly distributed around it’s mean, with greater probability density around the mean, and less as the values stray from the mean.
What value do we get if we sum up all the area in a normal distribution including negative values?
The mean. Values on either side will cancel out.
What is the blob rule?
The blob rule means that in E(x) = integral of x fx(x) dx, x can be replaced with anything, allowing us to get the area of any equation by integrating it.
what is expected value of (x - expected x)^3 a good measure of?
Graph skew. A long tail to the right gives a positive skew, a long tail to the left gives a negative skew.
What is a lognormal?
A lognormal is related to the standard normal, but has no negative values, and strong positive skew.
