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1. Probability Theory- Standard Normal Distributions

Homework Statement Two types of coins are produced at a factory: a fair coin and a biased one that comes up heads 55 percent of the time. We have one of these coins but do not know whether it is a fair coin or a biased one. In order to ascertain which type of coin we have, we shall...
2. Advice on finding math specialization

I'll be graduating in the fall with my b.s. in math and I'd like to continue on to graduate school. I would feel better about it though if I had a clue what particular area of mathematics I wanted to specialize in. So far, in my undergraduate career, I've gotten a good working overview of the...
3. Induction to show n!/(n^n) is less than .5^k

Homework Statement Show that \frac{n!}{n^n} \leq \frac{1}{2}^k for all n \geq 2, where k is the greatest integer less than or equal to n/2. Homework Equations Mathematical Induction The Attempt at a Solution I've shown the base case, and I've assumed that the hypothesis is true...
4. Optics Question

Hey, so i've got a HW for an optics lab and haven't studied optics for a while, so I could use a little help. The problem is a lensmaker's equation question involving a system of optical devices. An object at a distance of 30cm to the left of a converging lens of focal lenght +30cm...
5. Intro electric field question

I am just reviewing some E&M because i took the class before I ever thought i had that big of an interest in physics and just memorized formulas, etc. Anyway, this is from a "which of the following statements is true" question. The true statement is: A positive charge experiences an...
6. Estimating a difficult volume

Imagine that you are free to choose any 3 vertices from a 4 x 4 x 4 grid that has 16 equally distributed vertices, as if made up of 16 1x1x1 cubes. Now, having chosen your 3 vertices, these 3 vertices each serve as the "middle" of a circular cylinder. By middle I mean it is located at half the...
7. Fusion scientists

Quick question. Are physicists and engineers who work on designing fusion reactors generally well versed in both inertial confinement fusion and magnetic confinement fusion, or are they two separate subfields altogether.
8. Designing a research topic

Hey. I've been given the opportunity to perform a physics experiment this summer, and I have free range over what type of experiment I choose to perform. I'm sure most physics majors wouldnt have a problem designing a project, but I am finding the task really difficult. So far I've only taken...
9. Stokes theorem help

Hi, i cant seem to figure out how stokes theorem works. I've run through a lot of examples but i still am not having any luck. Anyway, some advice on a particular problem would be greatly appreciated. The problem is: F(x,y,z) = <2y,3z,-2x>. The surface is the part of the unit...
10. Physics Green careers in physics

Are there any fields of physics that one can go into after getting a masters or a phd that merge together experimental or theoretical physics and directly tackling environmental problems. The only thing I could think of is fusion research, which could eventually lead to cleaner energy. More...