Question

Problem 5 The joint pdf of x1 and x2 is 0.2 0 0.2 X1=1 | 0.2 0.2 X1=3 | 0.2 a) Find marginal pdfs p1(x1) and p2(x2) b) Are x1 and x2 independent? c) Compute Efx1 + x2J d) Compute covfx,, x2) e) Compute vars5x1 - 6x2}

Answer 1

You just need to use the concept of marginal distribution and few formulas listed below -

$E[X] = \sum x_{i}f_{X}(x_{i})$

$E[X^2] = \sum x_{i}^{2}f_{X}(x_{i})$

$Var(X) = E[X^2] - (E[X])^2$