Ejercicio variables aleatorias y función de probab

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Variables aleatorias y funciones de probabilidad 
Técnicas de análisis de datos

Lina Lasso 
Natalia Jiménez 
Grupo 6
FULL NAME
Se lanzan dos dados y se define la variable aleatoria X:"Suma del resultado del lanzamiento de dos dados"  Describa la función de probabilidad P(X=x) y calcule el valor esperado y la varianza de esta variable aleatoria
S = {2,3,4,5,6,7,8,9,10,11,12}
2
4
6
5
3

8
11
10

9
12

P (X=3) = 
{(1,2) (2,1)}
= 2/36

P (X=2) = {(1,1)} = {(1/6) x (1/6)} =1/36
P (X=2) = {(1,1)} = {(1/6) x (1/6)} =1/36
P (X=3) = {(1,2) (2,1)}= 2/36
P (X=4) = {(1,3) (2,2) (3,1)} = 3/36
P (X=5) = {(1,4) (2,3) (3,2) (4,1)} = 4/36
P (X=6) = {(1,5) (2,4) (3,3) (4,2) (5,1)} = 5/36
P (X=7) = {(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)} = 6/36
P (X=8) = {(2,6) (3,5) (4,4) (5,3) (6,2)} = 5/36
P (X=9) = {(3,6) (4,5) (5,4) (6,3)} = 4/36
P (X=10) = {(4,6) (5,5) (6,4)} = 3/36 
P (X=11) = {(5,6) (6,5)} = 2/36
P (X=12) = {(6,6)} = 1/36
Función de probabilidad (X=x)
P (X=2) = {(1,1)} = {(1/6) x (1/6)} =1/36
P (X=3) = {(1,2) (2,1)}= 2/36
P (X=4) = {(1,3) (2,2) (3,1)} = 3/36
P (X=5) = {(1,4) (2,3) (3,2) (4,1)} = 4/36
P (X=6) = {(1,5) (2,4) (3,3) (4,2) (5,1)} = 5/36
P (X=7) = {(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)} = 6/36
P (X=8) = {(2,6) (3,5) (4,4) (5,3) (6,2)} = 5/36
P (X=9) = {(3,6) (4,5) (5,4) (6,3)} = 4/36
P (X=10) = {(4,6) (5,5) (6,4)} = 3/36 
P (X=11) = {(5,6) (6,5)} = 2/36
P (X=12) = {(6,6)} = 1/36
Valor esperado
E (X) = 7
E(X=2) = 2 x 1/36
E(X=3) = 3 x 2/36
E(X=4) = 4 x 3/36
E(X=5) = 5 x 4/36
E(X=6) 6 x 5/36
E(X=7)= 7 x 6/36
E(X=8) = 8 x 5/36
E(X=9) = 9 x 4/36 
E(X=10) = 10 x 3/36
E(X=11) = 11 x 2/36
E(X=12) = 12 x 1/36
Varianza 
Var(X) = 5,83
Var(X=2) = (2-7)^2 x 1/36
Var(X=3) = (3-7)^2 x 2/36
Var(X=4) = (4-7)^2 x 3/36
Var(X=5) = (5-7)^2 x 4/36
Var(X=6) = (6-7)^2 x 5/36
Var(X=7) = (7-7)^2 x 6/36
Var(X=8) = (8-7)^2 x 5/36 
Var(X=9) = (9-7)^2 x 4/36 
Var(X=10) = (10-7)^2 x 3/36
Var(X=11) = (11-7)^2 x 2/36
Var (X=12) = (12-7) ^2 x 1/36

Ejercicio variables aleatorias y función de probab

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