Verify that f(x) = 2x/( k(k + 1)) for x = 1, 2, 3, . . . ,k can serve as the probability distribution of a random variable in a given range

If f(x) = 2x/k(k+1), x= 1, 2, 3,
4,....k.

To verify whether this is probability distribution
function, we should prove that {Sum f(x) over x = 1, 2, 3, 4,...k} =
1.

x takes a discrete value. That is x takes values like
 x= 1, 2, 3, 4, ......, k.

Let X be the random
variable

f(X =x) = 2x/k(k+1) = 2x/k(k+1), x= 1, 2, 3,
4....k.

Total frequency = {Sum f(X = x) , x= 1, 2, 3,
...n.} =
2*1/k(k+1)+2*2/k(k+1)+2*3/k9k+1)...2*k/k(k+1).

{Sum f(X =
x) , x= 1, 2, 3, ...n.} =
{2/k(k+1)}{1+2+3+..........k}

{Sum f(X = x) , x= 1, 2, 3,
...n.} = {2/k(k+1)}{Sum of the k natural numbers starting from
1}.

{Sum f(X = x) , x= 1, 2, 3, ...n.} =
{2/(k(k+1)}{k(+1)/2}

{Sum f(X = x) , x= 1, 2, 3, ...n.} =
1..

Therefore f(x) is a frequency density function. Or f(x)
is a probability distribution function.

What does "Bicameral Legislature" mean?

A bicameral legislature is one that is split up into two
houses.  Many legislatures around the world are split in this way.  For example, the
Congress of the United States is split up between the House of Representatives and the
Senate.

Bicameral legislatures are generally set up as a
way of providing checks and balances in a governmental system.  In a bicameral system
like that of the US, proposed bills must pass both houses of the legislature before they
can become law.  This makes it harder to pass legislation than it would be in a
unicameral (only one house of the legislature) system.

Determine if the line y+x-2 = 0 and the line 6y-3x +8 = 0 are parallel, perpendicular, or neither.

Given the lines:

y + x -2 =
0

6y-3x + 8 =0

We need to
determine the relation between the lines ( parallel, perpendicular, or
neither)

First we will use the slope to find the
relation.

If the slopes are equal, then the lines are
parallel.

if the product of the slopes is -1, then the
slope are perpendicular.

Let us rewrite the equations of
the lines into the slope form.

==> y = -x + 2
............(1)

==> y = (3/6)x -
8/6

==> y= (1/2)x -
4/3........(2)

We notice that the slopes are not equal.
then the lines are not parallel.

Also, the product of the
slopes is -1*1/2 = -1/2 , then the lines are not
perpendicular.

Then the slopes are not
parallel nor perpendicular.

In Book 13 of The Odyssey, why does Athena test Odysseus?

I think there are two elements two think about in
answering this question. Firstly, the gods in both The Iliad and The Odyssey are shown
to be quite a fickle group, using their human heroes to champion their petty squabbles
against other gods and treating them as playthings. Thus, in a sense, Athena can test
her hero because she is a goddess and she can do what she
likes.

However, also, it is important to remember what kind
of character Odysseus is. He is not known as "the wily Odysseus" for nothing, and
certainly throughout the rest of the book disguise, deception and illusion are used
readily and frequently to trick, beguile and deceive. Thus, there is something fitting
in Odysseus not realising he has reached Ithaca in this book: the deceiver is himself
deceived. Of course, once Odysseus realises his location, he immediately determines to
employ deception to achieve his goal until the grey-eyed goddess Athena reveals truth
through her own act of self-revelation.

What are some quotes that reflect images of sight/blindness, animals, and hell/demons from the play Othello?

One of the first, and a relatively famous animal quote is
from Iago as he calls up to Brabantio's house in the middle of the night in reference to
his daughter being with Othello: "Even now, no, very now, an old black ram Is tupping
your white ewe."  Of course he is trying to make the image as repellant as possible to
arouse anger in Brabantio and drive him to attack Othello the moor.  Just a little bit
later he says againto Brabantio:

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you'll have your daughter covered with a Barbary
horse, you'll have your nephews neigh to you, you'll have coursers for cousins, and
jennets for germans.

Pretty
nasty stuff!

A quote close by that reflects the idea of
vision or blindness is from the First Senator after the Duke asks him how it is possible
that the Turkish preparation makes for Rhodes rather than for Cyprus:  "'Tis a pageant
to keep us in false gaze" reflecting the idea that they have been looking the wrong
way.

How does my fake journal entry I wrote for Chris McCandless fit Chapter 16 of Into the Wild?My assignment was to write a poem, journal entry, or...

I like this initial response, and I think you have come up
with a number of great ideas. Here are a few more ideas to help you develop this
assignment and get an even better mark. You might want to develop what specifically
Chris learnt from his months of solitude and how he has changed as a result. It was
always his intention and dream to stay for longer in Alaska, so you need to explain
fully why he chose to attempt to leave earlier. You might even have him thinking about
some of the many characters he met along the way and thinking about those relationships
and how important they are to him, as he realises it
now.

Lastly, I would write a lot more about what Chris felt
and experienced when he tries to leave and can't. Would he berate himself for not
realising the impact of sping on the ice in Alaska? How would he feel? We are told later
by the author of this great book that if he had a map, he would have realised that he
could have crossed the river in another location, very close to where he was. Would he
wish that he had taken a map? I guess that having decided to make such a big decision,
and then to have that choice taken away from him, is going to make Chris feel upset,
frustrated and annoyed. You need to try and capture that in his
feelings.

Good luck, though! This is a great start and by
considering my questions you should be able to get a good grade.

Discuss Andrew Marvell as a metaphysical poet.

Andrew Marvell in his poem "To His Coy Mistress"
demonstrates two characteristics of poetry we, today, categorize as
metaphysical.

He uses stretched metaphors, for example.  In
part one of his syllogism, or logical argument designed to convince his target--a
woman--to sleep with him, he refers to their love as "vegetable love."  The idea is that
if they were immortal and could spend centuries in the wooing stage
of love making, their love could grow as slowly as a vegetable.  The metaphor is
stretched, of course.  The slow growing rate of a vegetable is not normally compared to
love growing.

Secondly, Marvell displays and revels in his
wit and intelligence and learning.  In the second part of his syllogism, in which he
centers on the mortality of humans, he concludes with

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The grave's a fine and private
place,

But none, I think, do there
embrace.

And later, in part
three, he says that the lovers should be like "amorous birds of
prey."

The grave couplet demonstrates his wit and keeps the
poem a little lighter than the morbid imagery might otherwise make
it.

The comparison of lovers to loving predators
demonstrates both a stretched metaphor and wit.

The
stretched metaphors, the wit displayed, and, additionally, the carpe diem theme, mark
Marvell as a metaphysical poet.