We define the stochasic variables Y₁ and Y₂ the following way:

Y₁: Hourly wage in period 1

Y₂: Hourly wage in period 2

The hourly wage in period 1 is normally distributed with a mean and variance2 which means:

Y₁N(,2)

The hourly wage in period 2 is given by:

Y₂ =+Y1+U where Y₁ and U are independent andUN(0,v2)

Questions

Assume that =0. Let=350 and 2=1123465. Also let=350(1) and v2=123465(12).

a) Give the marginal distributions of Y₁ and Y₂.

b) Show that for>0 , the following is true :E(Y2Y1=275)<E(Y2)

c) Now let =0.90. Calculate P(Y2275Y1275)andP(Y2425Y1275)

You can use the following results ( for when =0.90 )

P(Y1275,Y2275)0.193

P(Y1275,Y2425)0.250

d) Give a short interpretation of the results in b) and c).