If a needle is dropped into the square with side x, what is the probability that...
(8pts.) Let random variable X be the length of a side of a square. Suppose that X has the probability density function, f(x) = 1 / 2 0 < 252. (a) Find P(X < 0.5). (b) What is the variance of X? (C) Let Y be the volume of a cube built with the length of each side being X. Note that Y = X3. What is the expected volume of the cube, E(Y)?
A wire in the x−y plane is in the form of a square of side a and carries a counter-clockwise current I. What is B at the center of the square?
for a particle in a square box of side L, at what position is the probability density a maximum if the wave function has n1=1, n2=3? also describe the position of any node or nodes in the wave function.
This is a problem based on Buffon's needle problem. ( You can Google it) Suppose that M. Buffon’s floor is covered, not by unit width floor boards, but by a unit grid of square unit tiles. Suppose now that a unit length needle, (that is, a needle whose length is the length of the sides of these tiles), is dropped “randomly” on this floor. Calculate the probability that the needle crosses an edge of a tile. State clearly the probabilistic...
When you drop a matchbox onto the floor, there is a 15% probability of it landing on the side. Suppose the matchbox is dropped onto the floor 8 times. a) What is the probability of it NOT landing on the side on any the 8 times it's dropped? b) What is the probability that it will land on the side some of the times it's dropped? (one or more of the 8 times)
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1. The eigenfunctions of a particle in a square two-dimensional box with side lengths a = b = L are non, (x, y) = { sin ("T") sin (9,7%) = xn, (x)}n, (y) where n. (c) and on, (y) are one-dimensional particle-in-a-box wave functions in the x and y directions. a. Suppose we prepare the particle in such a way that it has a wave function V (2,y) given by 26,0) = Võru (s. 1) + Vedra ....
1. A square conductive loop of side 10.0 cm is centered in the x-y plane. It carries a 10.0 mA current clockwise when viewed from the +z direction. Find H(0, 0, 16 cm).
A target consists of a square region in which a quarter circle is drawn and shaded. The radius of the circle is equal to one side of the (T) by simulating darts being fired randomly at the target. A success is defined as a dart falling within the shaded area. If the computer obtains a value of 3.012 after 1000 shots at the target, how hitting the target is one. А square computer program calculates pi darts landed in the...
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
In class, we analyzed Buffon's needle experiment. We showed that if a large sheet of paper has parallel lines that are 1 inch apart, and we throw a needle of length 1/2 inch at it, the probability that the needle hits a line is l/r. We can estimate π by throwing many needles and seeing how many throws hit a line. Suppose we throw a needle n times, and each throw is independent. Let X be the number of throws...