If you were the attacker, and knew that your opponent was trying to maximize their probability of of successfully preventing your attack, how should you choose {qi} to maximize your probability of a successful attack? (Assume that your strategy is going to leak to your opponent.)

If q= (5p1+3p2) / (p1+p2) find dq/dp1 and dq/dp2

A sample of 500 students during the fall semester shows that 300 took ECON 201, 220 took MATH 126, and 80 students took both at the same time. What is the probability that a student took ECON 201 or MATH 126.

A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99