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

i think it is c, not positive though

step-by-step explanation:

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get