- #1
TomJerry
- 50
- 0
Question :
Random variate X follows a normal distribution with mean 0 and variance 1 i.e.X~N(0,1). Given Y = 2X + 4, find
i) E[Y]
ii) Var(Y)
iii) E[X^3]
Solution:
here E[X'] = 0 and V(X) = 1
i) E[Y] = E[2X+4] = 4 [Is this correct]
ii) Var(Y) = E[Y2] - [E(Y)]2
=E[Y2] -16
Now
E[Y2] = E[(2X+4)2]
= E[(4x2 + 16x + 16]
= 4 E[x2] + 16 E[x] + 16
= 4 E[x2] + 0 + 16
Stuck here ...how to evaluate E[x2]
Random variate X follows a normal distribution with mean 0 and variance 1 i.e.X~N(0,1). Given Y = 2X + 4, find
i) E[Y]
ii) Var(Y)
iii) E[X^3]
Solution:
here E[X'] = 0 and V(X) = 1
i) E[Y] = E[2X+4] = 4 [Is this correct]
ii) Var(Y) = E[Y2] - [E(Y)]2
=E[Y2] -16
Now
E[Y2] = E[(2X+4)2]
= E[(4x2 + 16x + 16]
= 4 E[x2] + 16 E[x] + 16
= 4 E[x2] + 0 + 16
Stuck here ...how to evaluate E[x2]