In a poker hand consisting of 5 cards, find the probability of holding (a) 3 aces (b) 4 hearts and 1 club (c) Cards of same suit (d) 2 aces and 3 jacks

Annabathuni Seethu keerthana
2022-07-24

In a poker hand consisting of 5 cards, find the probability of holding (a) 3 aces (b) 4 hearts and 1 club (c) Cards of same suit (d) 2 aces and 3 jacks

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asked 2022-07-03

What is the difference between multi-task lasso regression and ridge regression? The optimization function of multi-task lasso regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}\sum _{i=1}^{{N}_{t}}{J}^{l}(w,x,y)+\gamma \sum _{l=1}^{L}||{w}^{l}|{|}_{2}$

while ridge regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}{J}^{l}(w,x,y)+\gamma ||{w}^{l}|{|}_{2}$

which looks the same as the ridge regression. As for me, the problem of multi-task lasso regression is equivalent to solve global ridge regression. So what is the difference between these two regression methods? Both of them use ${L}_{2}$ function. Or does it mean that in multi-task lasso regression, the shape of $W$ is (1,n)?

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}\sum _{i=1}^{{N}_{t}}{J}^{l}(w,x,y)+\gamma \sum _{l=1}^{L}||{w}^{l}|{|}_{2}$

while ridge regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}{J}^{l}(w,x,y)+\gamma ||{w}^{l}|{|}_{2}$

which looks the same as the ridge regression. As for me, the problem of multi-task lasso regression is equivalent to solve global ridge regression. So what is the difference between these two regression methods? Both of them use ${L}_{2}$ function. Or does it mean that in multi-task lasso regression, the shape of $W$ is (1,n)?

asked 2022-06-15

regression $x(t)=at+b$, number of trials, and ${R}_{2}$ of the regression. How do I find the value and $95\mathrm{\%}$ confidence interval for the value of $V=x/t$?

asked 2022-08-09

A random sample of size $n$ from a bivariate distribution is denoted by $({x}_{r},{y}_{r}),r=1,2,3,...,n$. Show that if the regression line of $y$ on $x$ passes through the origin of its scatter diagram then

$\overline{y}\sum _{r=1}^{n}{x}_{r}^{2}=\overline{x}\sum _{r=1}^{n}{x}_{r}{y}_{r}$

where $(\overline{x},\overline{y})$ is the mean point of the sample.

$\overline{y}\sum _{r=1}^{n}{x}_{r}^{2}=\overline{x}\sum _{r=1}^{n}{x}_{r}{y}_{r}$

where $(\overline{x},\overline{y})$ is the mean point of the sample.

asked 2022-06-04

Short version, I need to find a regression to this: $a\equiv t\phantom{\rule{0.444em}{0ex}}(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}\mathrm{\Delta})$, $a$ and $\mathrm{\Delta}$ are the unknowns constants.

Any idea where I should start looking?

Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events ${t}_{i}$ for some real time musical analysis. They have a typical interval of $\mathrm{\Delta}$, but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, ${t}_{n+1}-{t}_{n}$ may be $0$ or any $m\mathrm{\Delta}$.

Any idea where I should start looking?

Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events ${t}_{i}$ for some real time musical analysis. They have a typical interval of $\mathrm{\Delta}$, but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, ${t}_{n+1}-{t}_{n}$ may be $0$ or any $m\mathrm{\Delta}$.

asked 2022-05-24

Is there a method for polynomial regression in $$2D$$ dimensions (fitting a function $$f(x,y)$$ to a set of data $$X,Y$$, and $$Z$$)? And is there a way to apply a condition to the regression in $$2D$$ that requires all functions fitted to go through the axis line $$x=0$$?

asked 2022-06-29

Show how the nonlinear regression equation $y=a{X}^{B}$ can be converted to a linear regression equation solvable by the method of least squares.

asked 2022-05-28

A similarity/metric learning method that takes in the form of ${x}^{T}Wy=z$, where $x$ and $y$ are real valued vectors. For example, two images.

Breaking it into a more familiar form:

${x}^{T}Wy=\sum _{ij}{w}_{ij}{x}_{i}{y}_{j}=z$

This essentially looks very similar to polynomial regression with only interactions between features (without the polynomials). i.e.

$z={f}_{w}(x)=\sum _{i}{w}_{i}{x}_{i}+\sum _{i}\sum _{j=i+1}{w}_{ij}{x}_{i}{x}_{j}$

I was curious to see if the optimization for the matrix $W$ is the same as doing optimization for multivariate linear/polynomial regression, since $x$ and $y$ are fixed, and the only variate is the weight matrix $W$?

Breaking it into a more familiar form:

${x}^{T}Wy=\sum _{ij}{w}_{ij}{x}_{i}{y}_{j}=z$

This essentially looks very similar to polynomial regression with only interactions between features (without the polynomials). i.e.

$z={f}_{w}(x)=\sum _{i}{w}_{i}{x}_{i}+\sum _{i}\sum _{j=i+1}{w}_{ij}{x}_{i}{x}_{j}$

I was curious to see if the optimization for the matrix $W$ is the same as doing optimization for multivariate linear/polynomial regression, since $x$ and $y$ are fixed, and the only variate is the weight matrix $W$?