x is a random variable with with a positive mean and for which E[x(x+1)]=80 and Var(x)=50. what is E[x]
Solution:
E[x(x+1)] = 80
E[x2 + x ] = 80
E[x2 ] + E[x] = 80
E[x2 ] = 80 - E[x]
Now, we know that
Var(x) = E[x2 ] - [E(x)]2
50 = 80 - E[x] - [E(x)]2
[E(x)]2 + E[x ] -30 = 0
The roots of this quadratic equations are 6 and -5
But it is given that the mean of x is positive.i.e. E[x ] is positive.
E[x ] = 6
x is a random variable with with a positive mean and for which E[x(x+1)]=80 and Var(x)=50....
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