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Considera el proceso suma $(S_n)_{n \in \mathbb{N}}$ donde $$S_n = X_1 + \dots + X_n$$ y $(X_n)_{n \in \mathbb{N}}$ es un proceso IID (variables independientes e idénticamente distribuidas), con distribución de probabilidad común dada por $$p(x) = \begin{cases} p & \text{si } x = 1 \\ 1-p & \text{si } x = -1 \\ 0 & \text{en otro caso} \end{cases}$$ y encuentra las funciones de momento del proceso suma: $\mu(t), \sigma^2(t), \sigma(t), R(t_1, t_2), C(t_1, t_2)$ y $\rho(t_1, t_2)$. Usar $$LaTeX$$ para escribir tus procedimientos matemáticos.

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Which type of bone development begins within a piece of cartilage? Endochondral ossification Intramembranous ossification Callus formation Osteoporosis

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Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. Vertex at ($-1, -3$), focus at ($0, -3$)

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1) Below are the prices of snowboards at two competing snowboard stores: (Choose one) Middletown Snowboards 345, 350, 356, 360, 375, 405 Snowboard Central 343, 370, 386, 392, 395, 402 a) Draw two box-and-whisker plots, one above the other, one for each store. Make sure to show an appropriate scale for your axis. b) What is the median price for a snowboard at Middletown Snowboards? c) What is the lowest price you could pay for a snowboard at Snowboard Central? d) What is the most expensive board at Middletown Snowboards? e) What is the range of prices for snowboards at Snowboard Central? f) Which price represents the 75th percentile for Middletown Snowboards? g) Which store would you rather buy a snowboard from? Why?

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2.23 Determine whether or not each of the following LTI systems is (i) causal and/or (ii) BIBO stable. If the system is not BIBO stable, provide an example of a bounded input that yields an unbounded output. (a) $y(t) = \frac{dx}{dt}$ (b) $y(t) = \int_{-\infty}^{t} x(\tau) \,d\tau$ (c) $y(t) = \int_{-\infty}^{t} x(\tau) \cos(t - \tau) \,d\tau$ *(d) $y(t) = x(t + 1)$ (e) $y(t) = \int_{t-1}^{t+1} x(\tau) \,d\tau$ (f) $y(t) = \int_{t}^{\infty} x(\tau) e^{2(1-\tau)} \,d\tau$

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A fair die is rolled once. Find the probabilities of the given events. Leave your answer as a fraction in the simplest form. a. The number rolled is a 3. b. The number rolled is odd. c. The number rolled is at least 1. Submit Question

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Consider a complex inner product space with norm induced by the inner product. If x and y are members of the space, prove that $(x, y) - (y, x) = \frac{i}{2} (||x + iy||^2 - ||x - iy||^2)$ and $(x, y) + (y, x) = \frac{1}{2} (||x + y||^2 - ||x - y||^2)$

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(5 points) Complete the MATLAB code using the following algorithm: a. prompt for the radius of a sphere (disregard units) b. calculate the volume of the sphere: $V = \frac{4}{3}\pi r^3$ c. output the result as a real number (do not use the general format) clc clear

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Write the name of the connective tissue type that matches each description. A connective tissue can be used more than once. 1. Contains elastic fibers and is found in the lungs. This tissue allows the lungs to inflate during inhalation and return to their original shape after exhaling. 2. Packed with parallel bundles of collagen fibers and found in tendons. This tissue resists pulling forces applied by muscles. 3. Has a firm, gelatinous ground substance containing collagen fibers. This tissue is found in the tracheal wall to support and prevent the trachea from collapsing. 4. Found under covering and lining epithelium. Its extracellular matrix contains a loose arrangement of fibers, and its viscous ground substance facilitates the flow of interstitial fluid containing nutrients to epithelial tissues. It also cushions and supports epithelia. 5. Contains many elastic fibers in a firm gelatinous ground substance. Located in external ear, auditory tube, and epiglottis. 6. Hard extracellular matrix forms trabeculae. 7. Forms a framework in the spleen, bone marrow, and lymph nodes. It contains fine, branching fibers. 8. Is packed with bundles of collagen fibers running in different directions. It is found in skin and allows skin to resist pulling forces from many different directions. 9. Fluid extracellular matrix used to transport substances throughout the body. 10. Contains a large number of lipid-storing cells. It is found throughout the body, cushions and insulates organs, and stores lipids for future energy needs.

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Question 14 PL AS1 AD2 AD1 0 Q2 Q1 RGDP (A) PL AS2 AS1 P2 P1 b a AD1 0 Q2 Q1 RGDP (B) PL AS1 AS2 b P1 a c AD1 AD2 0 Q1 Q2 RGDP (C) Refer to the above diagrams, in which AD1 and AS1 are the "before" curves and AD2 and AS2 are the "after" curves. A recession is depicted by: panel (A) only. panel (B) only. panel (C) only. panels (A) and (B).

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michele l.