The n candidates for a job have been ranked 1, 2, 3,..., n. Let X 5 the rank of a randomly selected candidate, so that X has pmf p(x)551yn x51,2,3,...,n 0 otherwise (this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: The sum of the first n positive integers is n(n 1 1)y2, whereas the sum of their squares is n(n 1 1)(2n 1 1)y6.]

Question:

The n candidates for a job have been ranked 1, 2, 3,..., n.  Let x = rank of a randomly selected candidate, so that x has pmf:

(this is called the discrete uniform distribution).

Compute E(X) and V(X) using the shortcut formula.

[Hint: The sum of the first n positive integers is , whereas the sum of their squares is

or

Step-by-step explanation:

Given

PMF

Required

Determine the E(x) and Var(x)

E(x) is calculated as:

This gives:

From the hint given:

So:

Var(x) is calculated as:

Calculating:

Using the hint given:

So:

So:

Take LCM

Apply difference of two squares

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

c) yes, because of asa or aas