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Консультация № 188334
06.12.2015, 06:18
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас помочь в решении задачи :Независимые случайные величины ХиУ заданы следующими законами:
Х -3 0 1 2 У -1 0 3
Р 0,5 0,3 0,1 0,1 Р 0,31 0,34 0,35
Укажите законы распределения случайной величины Х+У,Х-У и найдите их математическое ожидание и дисперсию.
Х -3 0 1 2 У -1 0 3
Р 0,5 0,3 0,1 0,1 Р 0,31 0,34 0,35
Укажите законы распределения случайной величины Х+У,Х-У и найдите их математическое ожидание и дисперсию.
Обсуждение
06.12.2015, 17:51
общий
это ответ
Здравствуйте, Эльвира!
X Y X+Y X-Y P
-3 -1 -4 -2 0.5*0.31=0.155
-3 0 -3 -3 0.5*0.34=0.17
-3 3 0 -6 0.5*0.35=0.175
0 -1 -1 1 0.3*0.31=0.093
0 0 0 0 0.3*0.34=0.102
0 3 3 -3 0.3*0.35=0.105
1 -1 0 2 0.1*0.31=0.031
1 0 1 1 0.1*0.34=0.034
1 3 4 -2 0.1*0.35=0.035
2 -1 1 3 0.1*0.31=0.031
2 0 2 2 0.1*0.34=0.034
2 3 5 -1 0.1*0.35=0.035
P(X+Y=0)=0.175+0.102+0.031=0.308
P(X+Y=1)=0.034+0.031=0.065
X+Y -4 -3 -1 0 1 2 3 4 5
P 0.155 0.17 0.093 0.065 0.308 0.034 0.105 0.035 0.035
P(X-Y=-3)=0.17+0.105=0.275
P(X-Y=-2)=0.155+0.035=0.19
P(X-Y=1)=0.093+0.034=0.127
P(X-Y=2)=0.031+0.034=0.065
X-Y -6 -3 -2 -1 0 1 2 3
P 0.175 0.275 0.19 0.035 0.102 0.127 0.065 0.031
M(X)=-3*0.5+0*0.3+1*0.1+2*0.1=-1.2
M(Y)=-1*0.31+0*0.34+3*0.35=0.74
M(X+Y)=M(X)+M(Y)=-1.2+0.74=-0.46
M(X-Y)=M(X)-M(Y)=-1.2-0.74=-1.94
D(X)=M(X^2)-M(X)^2=(-3)^2*0.5+0^2*0.3+1^2*0.1+2^2*0.1-(-1.2)^2=3.56
D(Y)=M(Y^2)-M(Y)^2=(-1)^2*0.31+0^2*0.34+3^2*0.35-(0.74)^2=2.9124
D(X+Y)=D(X)+D(Y)=3.56+2.9124=6.4724
D(X-Y)=D(X)+D(Y)=3.56+2.9124=6.4724
X Y X+Y X-Y P
-3 -1 -4 -2 0.5*0.31=0.155
-3 0 -3 -3 0.5*0.34=0.17
-3 3 0 -6 0.5*0.35=0.175
0 -1 -1 1 0.3*0.31=0.093
0 0 0 0 0.3*0.34=0.102
0 3 3 -3 0.3*0.35=0.105
1 -1 0 2 0.1*0.31=0.031
1 0 1 1 0.1*0.34=0.034
1 3 4 -2 0.1*0.35=0.035
2 -1 1 3 0.1*0.31=0.031
2 0 2 2 0.1*0.34=0.034
2 3 5 -1 0.1*0.35=0.035
P(X+Y=0)=0.175+0.102+0.031=0.308
P(X+Y=1)=0.034+0.031=0.065
X+Y -4 -3 -1 0 1 2 3 4 5
P 0.155 0.17 0.093 0.065 0.308 0.034 0.105 0.035 0.035
P(X-Y=-3)=0.17+0.105=0.275
P(X-Y=-2)=0.155+0.035=0.19
P(X-Y=1)=0.093+0.034=0.127
P(X-Y=2)=0.031+0.034=0.065
X-Y -6 -3 -2 -1 0 1 2 3
P 0.175 0.275 0.19 0.035 0.102 0.127 0.065 0.031
M(X)=-3*0.5+0*0.3+1*0.1+2*0.1=-1.2
M(Y)=-1*0.31+0*0.34+3*0.35=0.74
M(X+Y)=M(X)+M(Y)=-1.2+0.74=-0.46
M(X-Y)=M(X)-M(Y)=-1.2-0.74=-1.94
D(X)=M(X^2)-M(X)^2=(-3)^2*0.5+0^2*0.3+1^2*0.1+2^2*0.1-(-1.2)^2=3.56
D(Y)=M(Y^2)-M(Y)^2=(-1)^2*0.31+0^2*0.34+3^2*0.35-(0.74)^2=2.9124
D(X+Y)=D(X)+D(Y)=3.56+2.9124=6.4724
D(X-Y)=D(X)+D(Y)=3.56+2.9124=6.4724
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