# Questions tagged [self-study]

A routine exercise from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

6,140 questions
37 views

### Moment inequality: $E\mid X_1 X_2 X_3\mid \leq (E(\mid X_1\mid^3)+E(\mid X_2\mid^3)+E(\mid X_3\mid^3))/3$ for zero-mean r.v.'s?

Let $X_1, X_2, X_3$ be zero mean random variables and assume $E(\mid X_i \mid ^{4+\delta})\leq C, i=1,2,3$ where $C$ is a constant and $\delta>0$ some positive small constant. How can I show that ...
31 views

36 views

### How to show a UMVUE exists only if $g(p)$ is a polynomial of degree at most $n$?

Let $X\sim Bin(n,p)$. The problem is to show that a UMVUE can exist for $g(p)$ only if $g(p)$ is a polynomial in $p$ of degree at most $n$. For the case when $g(p) = \frac{1}{p}$ we can show that it ...
22 views

### ROC curve with symmetrical kernel

I am trying to use kernels with ROC curve, and 'm succeed to plot them but now my query is about theoretical grounds, i.e. its bias, var, etc. I want to evaluate the theorems (1 & 2) in Pulit (...
23 views

### How do we obtain the canonical parameter from the variance function in the context of exponential family distributions?

I am assuming the following definition of the exponential family: \begin{align*} f(y,\theta,\phi) = \exp\left\{\phi[y\theta - b(\theta)] + c(y,\phi)\right\} \end{align*} In such context, the variance ...
10 views

### If I wanted to see if their was a difference between two groups and paired each person with someone of similar age what test would I do?

I was thinking of doing a paired samples t-test, since we are pairing specific individuals from each group with each other. Is this correct?
28 views

39 views

### Stationary Process Ergodicity

Can you give me an example of a stationary nonergodic stochastic process that is time continuous?
68 views

### pdf from a set of conditional pdfs

I have an interesting problem, i have seen in many text books ways of calculating conditional pdfs but not many where given a set of conditional pdfs for a variable we wish to calculate it's pdf. In ...
15 views

### Condensing values of categorical data

Beginner ML question here. I have a dataframe with a categorical column, a lot of the values are slightly different but essentially mean the same thing. Here's an example of such values: ...