In example 10.4, we saw that our estimates of the individual lag coefficients in a distrib- uted lag model were very imprecise. one way to alleviate the multicollinearity problem is to assume that the dj follow a relatively simple pattern. for concreteness, consider a model with four lags: yt 5a0 1d0zt 1d1zt21 1d2zt22 1d3zt23 1d4zt24 1ut. now, let us assume that the dj follow a quadratic in the lag, j: dj 5g0 1g1j1g2j2, for parameters g0, g1, and g2. this is an example of a polynomial distributed lag (pdl) model. (i) plug the formula for each dj into the distributed lag model and write the model in terms of the parameters gh, for h 5 0,1,2. (ii) explain the regression you would run to estimate the gh. (iii) the polynomial distributed lag model is a restricted version of the general model. how many restrictions are imposed

In three to four sentences, explain the effect of a price ceiling on the quantity of a good and who this intervention intends to assist

During january 2018, the following transactions occur: january 1 purchase equipment for $20,600. the company estimates a residual value of $2,600 and a five-year service life. january 4 pay cash on accounts payable, $10,600. january 8 purchase additional inventory on account, $93,900. january 15 receive cash on accounts receivable, $23,100 january 19 pay cash for salaries, $30,900. january 28 pay cash for january utilities, $17,600. january 30 firework sales for january total $231,000. all of these sales are on account. the cost of the units sold is $120,500. the following information is available on january 31, 2018. depreciation on the equipment for the month of january is calculated using the straight-line method. the company estimates future uncollectible accounts. at the end of january, considering the total ending balance of the accounts receivable account as shown on the general ledger tab, $4,100 is now past due (older than 90 days), while the remainder of the balance is current (less than 90 days old). the company estimates that 50% of the past due balance will be uncollectible and only 3% of the current balance will become uncollectible. record the estimated bad debt expense. accrued interest revenue on notes receivable for january. unpaid salaries at the end of january are $33,700. accrued income taxes at the end of january are $10,100

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.