Recent content by Hiche

I'm not sure if this is the right place to ask.. Anyway. Assume we have some integral I with 0 and 2 as limits. I = 3∫xexdx from 0 to 2. What exactly do we have to do to find the partition points (and what are they?) but using the composite trapezoidal rule? I = 25.1671683 upon computing...

more than "two standard deviations away from its mean" Suppose we need to find the probability that a binomial random variable with n = 100 and p = 0.5 is more than two standard deviations away from its mean and then compare this to the upper bound given by Chebyshev's Theorem. What is...

Homework Statement A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine...

P(A U B) = P(A) + P(B) - P(A intersection B) = 3/4 + 1/3 - P(A intersection B) = 13/12 - P(A intersection B). So, when P(A intersection B) = 1/12, P(A U B) = 1 and when it's 1/3, P(A U B) = 3/4. Does it have to do something with that? It looks too obvious but I'm not figuring it out!

Okay thanks, but shouldn't p = 5/23? The total number of balls is 23.

Homework Statement If X is a discrete random variable with mean u = 12 and variance = 9, use Chebyshev's Theorem to find an upper bound for P(X = 21). Homework Equations The Attempt at a Solution Now, I'm not sure about this since there are different upper bounds, right...

Homework Statement We roll a fair die until we get a three or a four. Z denotes the number of rolls needed. What is the probability that Z >= 3? (replacement assumed) Homework Equations Geometric distribution seems logical here? The Attempt at a Solution Let p(A) = p(getting a...

Homework Statement We have an urn with 5 red and 18 blues balls and we pick 4 balls with replacement. We denote the number of red balls in the sample by Y. What is the probability that Y >=3? (Use Binomial Distribution) Homework Equations The Attempt at a Solution Okay, so we...

ydx = - (1 + e^x)dy then \frac{dx}{-(1 + e^x)} = \frac{dy}{y} This is separable, right? Or you are required to use a substitution?

We have this system of equations: \begin{cases} x'= -x + 2y & (1)\\ y' = -2x - y + e^{-t} & (2) \end{cases} where x(0) = 0 ; y(0) = 0 We apply the Laplace transform on (1) and (2) and get: (s + 1)X - 2Y = 0\\ 2X + (s + 1)Y = \frac{1}{s + 1} We can use elimination here...

Homework Statement Use the substitution x = e^t to solve the following differential equation in terms of Bessel functions: \frac{d^{2}y}{dt^2} + (e^{2t} - \frac{1}{4})y = 0 Homework Equations The Attempt at a SolutionSo, using the Chain Rule, \frac{d^{2}y}{dt^2} = e^{2t}\frac{d^{2}y}{dx^2} =...

Okay, so I tried solving it. 1/s(s^2 + 1) = 1/s - s/(s^2 + 1), and after a litle work, Y(s) = e^{-\pi s}/s - e^{-\pi s}/(s^2 + 1) - e^{-2\pi s}/s + e^{-2\pi s}/(s^2 + 1). Is this correct? Now, the Laplace inverse of Y(s) is \delta(t - \pi) - \delta(t - \pi)sin(t - \pi) - \delta(t - 2\pi) +...

We know that the \mathcal L\{f(t)\} = \int^{\infty}_0 e^{-st}f(t) dt. Say we want to, for example, solve the following IVP: y'' + y = f(t) where f(t) = \begin{cases} 0 & 0 \leq t < \pi \\ 1 & \pi \leq t < 2\pi\\ 0 & 2\pi \leq t \end{cases} and y(0) = 0 , y'(0) = 0 We apply Laplace on both...

Okay, so upon a little work, X_p = \begin{pmatrix}1\\2\end{pmatrix}t and the general solution is X = X_c + X_p Thank you, tiny-tim.

oh, crap! Apparently, 3 * 1 = 4 -_- So, again, the eigenvalues are \lambda_1 = -1 and \lambda_2 = 1. I hope this is correct. So the solution of X_c = c_1\begin{pmatrix}1\\1\end{pmatrix}e^t + c_2\begin{pmatrix}1\\3\end{pmatrix}e^{-t}. Now about X_p. Is my method correct (first post)?