Let X,YN(0,1) be two independent random variables. Complete the following exercises. (a) Define R, by the following equations: X=Rcos()Y=Rsin(). Use the transformation theorem to find the probability density function of R and . (b) Find the cumulative distribution function of R and . (c) Recall that if UUnif(0,1), and X is some random variable with known cumulative distribution function FX(x), then FX1(U) has the same distribution as X. Let U,VUnif(0,1) be two independent random variables. Find two functions g,h such that g(U) has the same distribution as R, and h(V) has the same distribution as . (d) Now we know that R=g(U),=h(V), find two functions , such that (U,V) and X have the same distribution and (U.V) and Y have the same distribution..

1. Marciano Manufacturing uses a standard cost system. Standards for direct materials are as
follows: Direct materials (pounds per unit of output) Cost per pound of direct materials $5 The
company plans to produce 3,500 units and has purchased on account 12,000 pounds of direct
materials at a net cost of $43,200. What is the journal entry to record this transaction?
Atoka Manufacturing uses a standard cost system. Standards for direct materials are as follows:
Direct materials (pounds per unit of output) Cost per pound of direct materials A. a debit to
Work - in - Process Inventory for $37,200, a credit to Raw Materials Inventory for $60,000, and
a debit to Direct Materials Efficiency Variance for $22,800 B. a debit to Work - in - Process
Inventory for $60,000, a credit to Raw Materials Inventory for $48,600, and a credit to Direct
Materials Efficiency Variance for $11,400 C. a debit to Work - in - Process Inventory for
$30,132, a credit to Raw Materials Inventory for $37,200, and a debit to Direct Materials
Efficiency Variance for $7,068 D. a debit to Work - in - Process Inventory for $30,132, a credit
to Raw Materials Inventory for $60,000, and a debit to Direct Materials Efficiency Variance for
$29,868