Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance.

Resolved: "Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the..."

kuCAu

2021-09-06

Suppose

E (X) = 5

and

E [X (X - 1)] = 27.5,

find

\in (x^{2})

and the variance.

averes8

Skilled2021-09-07Added 92 answers

We have the following properties:

E (X + Y) = E (X) + E (Y)

V (X) = E (X^{2}) - {[E (X)]}^{2}

So, if we have that

E [X (X - 1)] = 27.5,

we can write them using the first property as:

E (X (X - 1)) = 27.5

E (X^{2} - X) = 27.5

E (X^{2}) - E (X) = 27.5

Then, replacing

E (X)

by 5 and solving for

E (X^{2})

we get:

E (X^{2}) - 5 = 27.5

E (X^{2}) = 27.5 + 5

E (X^{2}) = 32.5

Finally, using the second property and replacing

E (X)

by 5 and

E (X^{2}) b y 32.5,

we get that

V (X)

is equal to:

V (X) = 32.5 - 5^{2}

V (X) = 32.5 - 25

V (X) = 7.5

Finally answer:

E (X^{2}) = 32.5

V (X) = 7.5

E [X (X - 1)] = E (X^{2}) - E (X)

V (X) = E (X^{2}) - {[E (X)]}^{2}

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