Considere a experi\u00eancia aleat\u00f3ria de espa\u00e7o de resultados S, que consiste no lan\u00e7amento de dois dados perfeitos e a vari\u00e1vel aleat\u00f3ria assim definida: \\[\\begin{array}{*{35}{l}}
\nX: & S\\to \\mathbb{R}\u00a0 \\\\
\n{} & (x,y)\\to x\\times 3y\u00a0 \\\\
\n\\end{array}\\]<\/p>\n
- \n
![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/dadosAV.jpg\" "\\"Dados\\"")
<\/a>Calcule:\n– $X((1,1))$
\n– $X((6,3))$
\n– $X((1,3))$
\n– $X((5,2))$<\/p>\ne indique o contradom\u00ednio de X.
\n(Para facilitar, construa uma tabela de dupla entrada.)<\/p>\n<\/li>\n- Construa a distribui\u00e7\u00e3o de probabilidades desta vari\u00e1vel aleat\u00f3ria.<\/li>\n
- Calcule:\n
– $P(X=6)$
\n– $P(X=12)$
\n– $P(X\\le 7)$
\n– $P(X>10)$<\/p>\n<\/li>\n- Calcule o valor m\u00e9dio e o desvio padr\u00e3o.<\/li>\n<\/ol>\n
Resolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n- \n
- <\/a>
\n\n\n
\n $x\\times 3y$<\/td>\n $y$<\/span><\/td>\n<\/tr>\n \n 1<\/td>\n 2<\/td>\n 3<\/td>\n 4<\/td>\n 5<\/td>\n 6<\/td>\n<\/tr>\n \n $x$<\/span><\/td>\n 1<\/td>\n 3<\/td>\n 6<\/td>\n 9<\/td>\n 12<\/td>\n 15<\/td>\n 18<\/td>\n<\/tr>\n \n 2<\/td>\n 6<\/td>\n 12<\/td>\n 18<\/td>\n 24<\/td>\n 30<\/td>\n 36<\/td>\n<\/tr>\n \n 3<\/td>\n 9<\/td>\n 18<\/td>\n 27<\/td>\n 36<\/td>\n 45<\/td>\n 54<\/td>\n<\/tr>\n \n 4<\/td>\n 12<\/td>\n 24<\/td>\n 36<\/td>\n 48<\/td>\n 60<\/td>\n 72<\/td>\n<\/tr>\n \n 5<\/td>\n 15<\/td>\n 30<\/td>\n 45<\/td>\n 60<\/td>\n 75<\/td>\n 90<\/td>\n<\/tr>\n \n 6<\/td>\n 15<\/td>\n 36<\/td>\n 54<\/td>\n 72<\/td>\n 90<\/td>\n 108<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n – $X((1,1))=1\\times (3\\times 1)=3$<\/p>\n
– $X((6,3))=6\\times (3\\times 3)=54$<\/p>\n
– $X((1,3))=1\\times (3\\times 3)=9$<\/p>\n
– $X((5,2))=5\\times (3\\times 2)=30$<\/p>\n
Na tabela ao lado, apresentam-se as imagens dos resultados da experi\u00eancia aleat\u00f3ria pela fun\u00e7\u00e3o X.<\/p>\n
O contradom\u00ednio da fun\u00e7\u00e3o X \u00e9: \\[D{{‘}_{X}}=\\left\\{ 3,6,9,12,15,18,24,27,30,36,45,48,54,60,72,75,90,108 \\right\\}\\]<\/p>\n<\/li>\n
- Na tabela seguinte, apresenta-se a distribui\u00e7\u00e3o de probabilidades desta vari\u00e1vel aleat\u00f3ria.
\n - Na tabela seguinte, apresenta-se a distribui\u00e7\u00e3o de probabilidades desta vari\u00e1vel aleat\u00f3ria.