Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

E(XY) = E(X) E(Y)
Cov(X, Y) = 0
Var (X + Y) = Var (X) + Var(Y)
E(X²Y²) = (E(X))² (E(Y))²

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : E(X2Y2) = (E(X))2 (E(Y))2

Explanation:

For X and Y be two independent random variables.

i) E(XY) = E(X) E(Y)

ii) Cov (X,Y) = E (XY) - E(X) E(Y) ⇒ E(X) E(Y) - E(X) E(Y) = 0

iii) Var (X + Y) = Var(X) + Var(Y)

iv) E(X²Y²) = E(X²) E(Y²)

∴ E(X²Y²) = E(X²) ⋅ E(Y²) is the incorrect option

4 views Answered 2022-09-04 04:29

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