Econ 2083 Dr. Saleheen Khan Spring 2011
Home assignment #3
1. Given that z is a standard normal random variable, compute the following probabilities. a. P(-1 z 0) b. P(-1.5 z 0) c. P(-2 z 0) d. P(-2.5 z 0) e. P(-3 z 0) 2. Given that z is standard normal r
Exercises. Double integrals.
Evaluate the following iterated integrals and sketch the region over which each integration takes place. 1. 2.
3.
dx (4 y
0 0
0 1 1 3 1 0
3
2
2
)dy
dy ( x + y + 1)dx
2
dx ( x
0 2 1
y 2 xy )dy
4. 5.
dy ( x
0 0
2
2
+ 2 y ) d
5. Double Integral. Now we consider theory of integration. As it was early we start from indenite integrals. Partial Antiderivatives. Let as given a two-variable function f (x, y ) on some rectangle Q = [a, b; c, d]. Considering it as the function of vari