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

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

idk

step-by-step explanation: