Probability and Statistics

ONLY HIGH QUALITY ANSWER WILL BE ACCEPTED, 20 MINUTES FROM NOW

Section 1

Explanation

Var(X) = E[X^2] - (E[x])^2=E((X-u)^2)

Var(aX+b) = a^2Var(X)

Var(X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

On the off chance that autonomous, simply the initial two

Cov(X,Y) = E[(X-E[X])(Y-E[Y])]=E(XY)- E(X)E(Y)

Section 2

Question:

chapter100

Right to a Hearing.Appellant claims that the district court erred in not conducting an evidentiary hearing. He is wrong. In the first place, motions do not usually culminate in evidentiary hearings.SeeFed.R.Civ.P. 43(e) (court may "hear" motion and determine ancillary facts on affidavits or depositions). Second, we regularly turn a deaf ear to protests that an evidentiary hearing should have been convened but was not, where, as here, the protester did not seasonably request such a hearing in the lower court. This appellant knows the rule at first hand.SeeAoude,862 F.2d at 894(a matter can adequately be "heard" on the papers so long as "the parties ha[d] a fair opportunity to present relevant facts and arguments to the court, and to counter the opponent's submissions") (discussing necessity for hearing on preliminary injunction);see alsoMorales-Feliciano v. Parole Board,887 F.2d 1, 7 (1st Cir.1989)(civil contempt finding does not require evidentiary hearing when none requested below);cf.Beaulieu v. United States Internal Revenue Service,865 F.2d 1351, 1352 (1st Cir.1989)("it is a party's first obligation to seek any relief that might fairly have been thought available in the district court before seeking it on appeal").

Question 1

Please what is (are) the likely cause(s) of sudden sharp but brief pain

(resembling pin prick) in the right lower abdomen?

Question 2

What are the causes of foot drop, and what is the likely treatment?

Question 3

What is the correct definition for dysaesthesia?

Question 4

What is the difference between 'light touch' and 'fine touch' sensations

passed in the posterior column, and which one of these is tested with a

wisp of cotton?

Question 5

What is apraxia of gait and what is Brun's apraxia?

Question 6

Why is it that, when eliciting the plantar reflex, we are supposed to stop

just before the ball of the great toe?

Question 7

Is there any rationale for giving dopamine agonists to aphasic

patients?

Question 8

Have either carbamazepine or dopamine agonists a role in the treatment

of aphasia? If yes, what type of aphasia?

Question 9

Is bilateral VIth cranial nerve palsy always a false-localizing sign

(i.e. does it indicate an increased intracranial pressure and not pathology

of the nerves or their nuclei)?

Question 10

Can an optic tract lesion, which is mononuclear field loss (i.e. loss

of vision in one eye) also be called 'incongruous homonymous