March 15 (Reuters) - Shares of Facebook Inc fell as much as 5 percent on Friday to their lowest in nearly three months after the surprise departure of Chief Product Officer Chris Cox, at a time when the company is again being scrutinized over its handling of privacy, extremism and political content. Cox, a Wall Street favorite who has worked with Facebook founder Mark Zuckerberg for 13 years, led the social network's business development team and helped define the business model of its messaging service WhatsApp. "We believe Cox played a critical role in establishing FB's mission, values, and culture, and he was extremely well-regarded inside and outside the company, including by Wall Street," JPMorgan analysts wrote in a research note. "The live-streaming of New Zealand's shooting will certainly bring on more questions of regulation and scrutiny over Facebook. It helped provide a platform for today's horrific attack and will undoubtedly be called into question for facilitating the spread of this," said Clement Thibault, analyst at global financial markets platform Investing.com.