Acertain college has m freshmen, m sophomores, m juniors, and m seniors. a certain class is a simple random sample of size n students, i. e., all sets of n of the 4m students are equally likely. let x1, . . , x4 be the numbers of freshmen, . . , seniors in the class.

(a) find the joint pmf of x1, x2, x3, x4.

(b) give both an intuitive explanation and a mathematical justification for whether or not the distri- bution from (a) is multinomial.

(c) find cov(x1, x3), fully simplified. hint: 1+x2+x3+x4 =n.

(d) how does cov(x1,x3) compare to if the distribution in (a) were multinomial? why does this make sense?

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

lol.

it's ok we all do this sometimes.

-aparri

answer: the is put the 450

step-by-step explanation: