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Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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The random variable X follows a Poisson process with the given value of and t. Assuming = 0.14 and t=14, compute the following.
(a) P(6)
(b) P(X <6)
(c) P(X≥6)
(d) P(4sXs6)
(e) x and x

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
The moment generating function of the random variable X is given by mx(s) = e2e-2 and the moment generating function of the random variable Y is my (s) = (et + )10. If it is assumed that the random variables X and Y are independent, find the following: (a) E(XY); (b) E[(X – Y)²] (c) Var(2X – 3Y).
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The random variable X follows a Poisson process with the given value of and t. Assuming A= 0.12 and t= 11, compute the following. (a) P(4) (b) P(X < 4) (c) P(X 2 4) (d) P(3 sXs7) (e) Hx and oy (a) P(4) 0.0338 (Do not round until the final answer. Then round to four decimal places as needed.) (b) P(X < 4) = 0.9549 (Do not round until the final answer. Then round to four decimal places as needed.) (c) P(X2 4) 0.0451 (Do not round until the final answer. Then round to four decimal places as needed.) (d) P(3 3XS7) (Do not round until the final answer. Then round to four decimal places as needed.) (e) Hx (Round to two decimal places as needed.) oy (Rasund to three decimal places as needed.)
(16) The moment-generating function of the geometric random variable X with parameter p is M(t) = 1-per. Use this to find the mean and variance of X.
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The PDF of the random variable XX is given below (1st figure). Suppose you have a random variable Y, where Y=aX+b, and whose PDF is given below (2nd figure). Determine the values of a and b.
Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27
Let X and Y denote two random variables. Which of the following can be used to compute Var(X)? A. E[Var(X|Y)] + Var(Var(X|Y)) B. E[E[X|Y]] + Var(Var(X|Y)) C. E[Var(X|Y)] + Var(E[X|Y]) D. Var(E[X|Y]) + Var(Var(X|Y))
For a random variable X, suppose that E[X] = 2 and Var(X) = 4. Then (a) E[(4 + x)²] =| (b) Var (5+5X): =
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