Tag: Math

# Confidence Interval of Normal Distribution

Ref: https://www.quora.com/What-is-the-difference-between-99-and-95-confidence-interval Confidence intervals are a little bit tricky in a sense that people don't define what they really mean by confidence interval. Now let me tell you a scenario using which you can start understanding CIs on a very basic level. Imagine you want to find the mean height of all the people in a … Continue reading Confidence Interval of Normal Distribution

# Z-Score

Z score normalize a distribution to a standard form of mean = 0, variance = 1. Z = (X-mean)/(standard variation)

# Intuitive Meaning of Covariance

Ref: http://stats.stackexchange.com/questions/18058/how-would-you-explain-covariance-to-someone-who-understands-only-the-mean Sometimes we can "augment knowledge" with an unusual or different approach. I would like this reply to be accessible to kindergartners and also have some fun, so everybody get out your crayons! Given paired (x,y)(x,y) data, draw their scatterplot. (The younger students may need a teacher to produce this for them. 🙂 Each pair … Continue reading Intuitive Meaning of Covariance

# Standard Deviation: Why divided by (n-1) and not n?

Ref: http://mathcentral.uregina.ca/RR/database/RR.09.95/weston2.html Suppose that I am interested in the number of hours per day that high school students in North America spend doing their mathematics homework. The "population" of interest is all high school students in North America, a very large number of people. Lets call this number N. My real interest is the mean and … Continue reading Standard Deviation: Why divided by (n-1) and not n?

# Sense of PCA, eigenvectors & eigenvalues

Ref: http://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues Imagine a big family dinner, where everybody starts asking you about PCA. First you explain it to your great-grandmother; then to you grandmother; then to your mother; then to your wife; finally, to your daughter (who is a mathematician). Each time the next person is less of a layman. Here is how the conversation … Continue reading Sense of PCA, eigenvectors & eigenvalues