Question

If x and y are two independent normal random distributions with mean and sd's are (10,5) and (15,12) these mean and sd of x+y is

Answer 1

Given :  x and y are two independent normal random distributions with mean and sd's are (10,5) and (15,12)  

To Find : mean and sd of x+y is

Solution:

Mean X = 10

SD  X = 5

Var X =  25

Mean Y  = 15

SD  Y  = 12

Var Y = 144

Mean X + y   =  10 + 15 = 25

Variance (X + Y)  = Var X  + Var Y

=> Variance (X + Y)  = 25 + 144

=> Variance (X + Y)  = 169

=> Variance (X + Y)  = 13²

=> SD ( X + Y)  = 12

mean and sd of x+y is   ( 25 , 13 )

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