Recent content by t.kirschner99

Thanks for the help on this question!

a) Yes, ln(x+y) does not equal ln(x) + ln(y), only ln(xy) = ln(x) + ln(y). Think that scribble on the bottom was my brain losing grasp of reality lol. b) ##\frac d{dx} e^{-n(x-β)}## = ##-n e^{-n(x-β)}##. Therefore, the anti-derivative is ##\frac {-1}{n} e^{-n(x-β)}##. c) Before getting to the...

Sorry about the quality of the photo. I'll include a new photo at the bottom of this post. For my strategy in this problem, the question asked for me to find the cutoff value using the Type I error of 0.05. Thus, I started with the Type I error definition which is... α = P(Reject Ho | Ho is...

I have added the whole problem to the original post. The Xmin formula was given to us in the question.

Homework Statement A random sample of X1, X2, · · · , Xn is taken from a population of values that is modeled by the following probability density function: f(xi; β) = e-(xi-β), xi≥β Suppose we test the hypothesis: Ho: β = 1 , HA: β > 1 a) Suppose you are to test the above hypothesis based...

Homework Statement Find the y-centroid of y=x3 between the x-axis, x=2, where area is 4. Homework Equations yc = integral of (ydA/A) dA = g(y)dy yc = h/2 * (n+1)/(2n+1) The Attempt at a Solution g(y) = y1/3 A = 4 yc = integral of (y*y1/3/4 dy) = integral(y4/3 * 1/4 dy) = 3/7 y7/3 * 1/4 Now...

Cannot edit my solution attempt, ignore what I put there. The Attempt at a Solution Questioning myself on strong induction, but I committed to it. Base case of 0 and 1 are good. Inductive Hypothesis: $$ a_k \leq 20k $$ Proof: Want to prove $$a_{k+1} \leq 20(k+1) $$ $$a_{k+1} = a_{\frac...

Homework Statement a0 = 0, and for n > 0, $$a_n = a_{\frac {n} {5}} + a_{\frac {3n} {5}} + n $$ For the above equation, besides an, the subscripts are floored Prove that an ≤ 20n Homework Equations See above. The Attempt at a Solution I know how to do the question, my problem is starting...

Ah thank you for opening my eyes! That would be equal to $$f_{k+2} $$ thus the statement is proven. One quick question about the hypothesis, would I need to assume that k > 3 ?

Homework Statement Define the Fibonacci Sequence as follows: f1 = f2 = 1, and for n≥3, $$f_n = f_{n-1} + f_{n-2}, $$ Prove that $$\sum_{i=1}^n f^{2}{}_{i} = f_{n+1} * f_{n} $$ Homework Equations See above. The Attempt at a Solution Due to two variables being present in both the Sequence...

Homework Statement Consider the IIR filter yn = xn - yn-2 State whether the filter is low, high, or band pass. Homework Equations The Z-transform: $$H(z) = \frac {1} {1+z^2},$$ Subbing ##z = e^{2πiw}## : $$H(w) = \frac {1} {1+e^{4πiw}},$$ Amplitude response: $$|H(w)| = \sqrt{{(\frac {1} {1...

Alright. Thanks for the help BvU! Really appreciate it!

Thanks. Based on the equation listed for A above (+inx), do you think I should be trying to find the inverse fourier?

That is what I thought. Thanks for the confirmation! Any idea on what kind of direction I take for A then? Combed through my notes and it only explains the process for B of course.

Homework Statement f(x) = -1, -π ≤ x ≤ 0 2, 0 ≤ x ≤ π Given this find the Fourier series using both $$a) \sum_{n=-∞}^\infty a_n e^{inx}$$ $$b) \sum_{n=0}^\infty [A_n cos(nx) + B_n sin(nx)]$$ Homework Equations $$a_o = \frac {1} {2L} \int_{-L}^L f(t) \, dt $$ $$a_n = \frac {1} {L}...