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!
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...
Homework Statement
The problem asks us to write a MATLAB function that takes as input a vector 'v' representing a 64-bit machine number in double precision, and extract the sign (t), the exponent (c), and the mantissa (f).
Homework Equations
The Attempt at a Solution
I'm extremely novice at...
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} =...
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...