Show that Cx = B 1Dt expa - x2 4Dt b is also a solution to Equation 5.4b. The parameter B is a constant, being independent of both x and t. Hint: From Equation 5.4b, demonstrate that 0c B 1Dt expa - x2 4Dt b d 0t is equal to D 0 2 c B 1Dt expa - x2 4Dt b d 0x2
Executive Memorandum Star Digital Frederick Eccher Star digital is a multichannel video service provider that spends more than 100,000,000.00 in advertising each year. Its advertising goals range from brand building to increasing package sales, most of its advertising dollars went to TV. Around 2012 they started increasing their spending in banner ad online advertising because of potential customers spent a significant amount of time online and customers were increasingly turning to the internet to consume products and services. Understanding demographics was easier with online advertising which was key to its spending decisions. In offline advertising it is generally true that half of the money spent on advertising is wasted, but the advertiser doesn’t know which half. Its nearly impossible to see the effectiveness of offline ads impressions and conversions versus relatively easy in the online advertising world as data is easier to obtain. But even with so much data it’s hard to measure ad effectiveness. Ads can be undervalued as they may drive someone to research the product before buying i.e. no click through or overvalued as an impression gets credit for helping a conversion regardless of whether the customer was interested or not. Star Digital did a display advertising experiment to test the later for more accurate ROI. The experiment measured the incremental impact of advertising on the outcome of sales. Users were assigned randomly to a test or control group. The control group saw charity ads and the test say star digital ads. The control group was a costly endeavor because it costs just as much as regular advertising. It was cut down to 4 factors in order to maximize profit while still conducting the experiment with valid results. The factors were: Baseline conversion rate, campaign reach, the minimum lift the advertiser cares to detect, and the power of the experiment. Which boils down to running a large campaign and using a small fraction to compare conversions vs the regular test group. So 10 percent was deemed an appropriate number to make the comparison while not losing to much value to the control group. 170 million impressions were made to 45 million users…. Boiling down to 4.5 million in the control group. Star Digital Test results purchase test imp_1 imp_2 imp_3 imp_4 imp_5 imp_6 From this you can see that advertising is effective and imp_6 seems to be one of the best buys with imp_1 doing well as well.