## Show the convergence of \$sum_{i=1}^{n}prod_{i=1}^{n}(X_{i})\$

P($$X_{i}$$=a)=P($$X_{i}$$=b)=0.5;

a*b=0.5;

$$Y_{i}$$=$$sum_{i=1}^{n}prod_{i=1}^{n}(X_{i})$$;

Does {$$Y_{i}$$}$$_{n=1}^{∞}$$ converge a.s. to some limit random variables? If yes, what is its mean and variance?

I think, without loss of generality, I can Let a=1,b=0.5 (P($$X_{i}$$=1)=P($$X_{i}$$=1/2)=0.5).

Then it’s obviously that $$Y_{i}$$ will converge, but how to find this limit?

If I let a=2,b=0.25, will it converge?

## SharePoint 2019 on premise – User Profile Sync – show user properties in people search display

Our user profile sync is working well.

What I am not able to see are additional properties. Any good information on this?

Any help appreciated.

## Does Ahrefs’ free backlink checker show accurate stats?

Does Ahrefs’ free backlink checker show accurate stats?

## does the joe biden/ Tara Reid fiasco show that rape is a core value of liberalism…?

Let’s not forget that Trump as well as many other politicians, rich, and famous people are known sexual predators that usually have little to no consequence for their actions. I don’t like liberals either, but the problem isn’t which political party has a “core value” of rape, it’s that those in power are often untouchable. When you mix politics in, people only care about what’s convenient to them. For example, I’ve been very outspoken about my distaste for both Biden and Trump and their history of sexual assault. Many of the people who applauded me for speaking against Trump’s actions are now accusing me of being an idiot and or a Trump supporter. They also accuse Tara Reid of lying when these are the same people who say that you should believe the victim until proven guilty of lying. This is because these people claim to care about sexual assault victims and “feminism” only when it’s politically convenient. Liberals want Trump out of the white house, but it’s not convenient to point out that his only competitor is just as bad as Trump (Democrats really shot themselves in the foot there but that’s a different topic), so suddenly their “morals” aren’t as important as they were before. I can say the same about Trump supporters as well. They don’t take too well to me pointing out his history but just loooove the fact that Biden did the same stuff. “Support” for sexual assault victims amongst many other people liberals claim to love is very flimsy, aye?

## real analysis – Show that if a function \$f\$ Lipschitz continuous on \$X\$, \$f\$ has to be uniformly continuous on \$X\$.

Show that if a function $$f$$ is Lipschitz continuous on $$X$$, $$f$$ has to be uniformly continuous on $$X$$.

My attempt:

(1) The definition of Lipschitz continuity for $$f$$ on $$X$$ is:

$$exists L in mathbb{R}^+_0 ,,,forall x,y in X: |f(x)-f(y)|le L |x-y|Longleftrightarrow frac{|f(x)-f(y)|}{|x-y|}le L$$

For the case $$L=0$$ it has to hold that $$,,forall x,y in X:|f(x)-f(y)|=0$$ this means the function is constant and therefore uniformly continuous.

Now let $$0ne L=frac{epsilon}{delta}$$ with two corresponding $$epsilon,deltainmathbb{R}^+$$ or in other words $$forall epsilon >0,,, existsdelta>0:frac{epsilon}{delta}=L$$

We now know $$frac{|f(x)-f(y)|}{|x-y|}le frac{epsilon}{delta}=L$$

that can only be true when $$forall epsilon >0,,, existsdelta>0,,,forall x,yin X:|x-y|

Which is the Heine-Cantor definition of uniform continuity.

So if $$f$$ isnt uniformly continuous, than $$f$$ also cannot be Lipschitz continuous.

Would be great if someone could look over it!

## woocommerce – Show a popup message before redirect

i just wrote this functions:

``````       add_action('woocommerce_before_single_product', 'product_out_of_stock_redirect');
function product_out_of_stock_redirect(){
global \$post;
global \$product;

\$terms = get_the_terms( \$post->ID, 'product_cat' );

foreach ( \$terms as \$term ) {
\$product_cat_id = \$term->term_id;
break;
}
\$terms1 = get_the_terms( \$post->ID, 'pa_marca' );

foreach ( \$terms1 as \$term1 ) {
\$marca = \$term1->name;
break;
}
\$marca = str_replace(".","-",\$marca);
\$marca = str_replace("https://wordpress.stackexchange.com/","-",\$marca);
\$marca = str_replace("'","",\$marca);
if (!\$marca) {
}
else { \$link = get_term_link( (int)\$product_cat_id, 'product_cat' ); \$link= \$link . "?filter_marca=" . \$marca;  }

if (!\$product->is_in_stock()){
wp_redirect( \$link, 301 );
exit(); // Always after wp_redirect() to avoid an error
}
}
``````

as you can see this simply functions redirects all user that visit an outofstock products to another page.
But i need to add an alert to keep user informated of that…how can i add a simply popup that alerts an user?

## 8 – How to show selected image in custom form Enitty Brower?

This is my custom form for showing media image.

``````   \$form['attributes']['image'] = [
'#type'          => 'entity_browser',
'#entity_browser' =>  'image_entity_browser',
'#cardinality' => 1,
'#selection_mode' => 'selection_append',
];
``````

How can I show my image like this after I selected? When I submit my image not show too.

## complexity theory – Show that recurrence is O(phi^logn)

I have a function whose time complexity is given by the following recurrence:

$$begin{equation*} T(n) = begin{cases} mathcal{O}(1) & text{for } n=0\ T(k)+T(k-1)+mathcal{O}(1) & text{for } n=2k\ T(k)+mathcal{O}(1) & text{for } n=2k+1\ end{cases} end{equation*}$$

and I have to prove that $$T(n)in mathcal{O}(phi^{log_2 n})$$

Where $$phi$$ is the golden ratio, $$(1 + sqrt5)over2$$

I think I could prove it by induction but, how would I go on about it if I didn’t know that $$T(n)in mathcal{O}(phi^{log_2 n})$$ in the first place?

Thanks!

## Show that a function f, continuous on (a,b), has an abs minimum value. The limits as x approaches either bounds of the interval is +Infinity

Can you show that the function f must have an absolute minimum value on the interval (a,b), if f is continuous on (a,b) and the right hand limit as x->a along with the left hand limit as x-> b are both equal to positive infinity?