Page 520 - flip-proba1

✐ ✐

“probMathBookFC” — 2019/2/9 — 17:32 — page 510 — #516
✐ ✐

510 C. Sugerencias a los ejercicios

2
c)CovpX, Y q“ 3{10 ´p9{16q “´0.01640625 .
d)CovpX, Y q“ 1.
e)CovpX, Y q“ 1{4.
500. a)CovpX, Y q“ ErpX ´ EpXqqpY ´ EpY qs
“ ErXY ´ XEpY q´ YEpXq` EpXqEpY qs
“ EpXY q´ EpXqEpY q´ EpY qEpXq` EpXqEpY q
“ EpXY q´ EpXqEpY q.
b)CovpX, Y q“ ErpX ´ EpXqqpY ´ EpY qqs
“ ErpY ´ EpY qpX ´ EpXqqs
“ CovpY, Xq.
c)CovpX, cq“ ErpX ´EpXqqpc´Epcqqs “ Erpc´EpcqqpX ´EpXqqs “ 0.
d)CovpcX, Y q“ ErpcX ´ EpcXqqpY ´ EpY qqs
“ ErcpX ´ EpXqqpY ´ EpY qqs
“ ErpX ´ EpXqqpcY ´ EpcY qqs
“ CovpX, cY q
“ cErpX ´ EpXqqpY ´ EpY qqs
“ c CovpX, Y q.

e)CovpX ` c, Y q“ ErpX ` c ´ EpX ` cqqpY ´ EpY qqs
“ ErpX ´ EpXqqpY ` c ´ EpY ` cqqs
“ CovpX, Y ` cq
“ ErpX ´ EpXqqpY ´ EpY qqs
“ CovpX, Y q.
f )CovpX 1 ` X 2 ,Y q“ ErpX 1 ` X 2 ´ EpX 1 ` X 2 qqpY ´ EpY qqs
“ ErpX 1 ´ EpX 1 q` X 2 ´ EpX 2 qqpY ´ EpY qqs
“ ErpX 1 ´ EpX 1 qqpY ´ EpY qq ` pX 2 ´ EpX 2 qqpY ´ EpY qqs
“ ErpX 1 ´EpX 1 qqpY ´EpY qqs`ErpX 2 ´EpX 2 qqpY ´EpY qqs
“ CovpX 1 ,Y q` CovpX 2 ,Y q.
2 2
g)VarpX ` Y q“ ErpX ` Y q s´rEpX ` Y qs
2 2 2 2
“ ErX ` 2XY ` Y s´ rE pXq` 2EpXqEpY q` E pY qs
2 2 2 2
“ EpX q´E pXq`EpY q´E pY q`2EpXY q´2EpXqEpY q
“ VarpXq` VarpY q` 2CovpX, Y q.
h)CovpX, Y q“ EpXY q´ EpXqEpY q“ EpXqEpY q´ EpXqEpY q“ 0.

✐ ✐

✐ ✐