1. If a pair of coils were placed around a homing pigeon and a magnetic field was applied that reverses the earth’s field, it is thought that the bird would be disoriented. Under these circumstances it is just as likely to fly in one direction as in any other. Let θ denote the direction in radians of the bird’s initial flight. θ is uniformly distributed over the interval [0, 2π]. (a) Find the density for θ. (b) Sketch the graph of the density. The uniform distribution is sometimes called the rectangular distribution. Do you see why? (c) Shade the area corresponding to the probability that a bird will orient within π/4 radians of home, and find this area using plane geometry. (d) Find the probability that a bird will orient within π/4 radians of home by integrating the density over the appropriate region(s), compare your answer to that obtained in part (c). (e) If 10 birds are released independently and at least 7 orient within π/4 radians of home, would you suspect that perhaps the coils are not disorienting the birds to the extent expected? Explain based on the probability of this occurring. 3. I haven't done the other parts because I'm stuck on finding the density for θ: Based on the pdf formula, I got this but I don't know what the f(x) dx part should be a. f(θ) = ∫2∏0 "f(x) dx?"