Shankar really likes playing Badminton. On a particular day at Fetzer gym he plays two games (whose outcomes are independent of each other). He has .3 probability of winning the first game and he has .9 probability of winning the second game. There are no ties and as stated above the outcomes of each game are independent of each other. Let X denote the number of games shankar wins.

Calculate E[X] and E[X2].

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Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?