x is a random variable with with a positive mean and for which E[x(x+1)]=80 and Var(x)=50....

Question

Question

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]

math Statistics-And-Probability

Answer 1

Answer #1

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

Answer 2

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