1. Find the density of Y = 1- e-AX when X ~Exp(X). Note that the density of X isde-dzif x > 0,f(x) :otherwise.What is the name of the distribution of Y?

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Answered: 1. Find the density of Y = 1- e-ax when…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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10. It is known that the probability of being able to log on to a computer from a re- mote terminal at any given time is .7. Let X denote the number of attempts that must be made to gain access to the computer. (a) Find the first four terms of the density table. (b) Find a closed-form expression for f(x). (c) Find P[X = 6]. (d) Find a closed-form expression for F(x). (e) Use F to find the probability that at most four attempts must be made to gain access to the computer.
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Let X have a pdf of f(x) = 4/15, 3 < X < b. a. What type of distribution does X have? b. Find b such that f(x) is a pdf. c. Find P(3.8 < X < 5.3). Give exact answer(fraction). d. Find μ, σ^2. Give exact answers(fractions).
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2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…
7. Radar returns (power) are modeled in terms of the following (gamma) density, x X f(x) = ² ² e ²³ U (x) B (a) What is the value of B so that f(x) is a valid pdf? (b) What is the probability that the received power exceeds 2 units. (c) What is the probability that the received power is less tha 6 units. (d) What is the probability that the received power lies between 2 and 6 units (e) What is the probability that the received power is exactly 5 units. (f) If past observations have shown that the received power is always more than 3 units, what is the probability that the the received power will be less than 6 units. (g) What is theprobability that X²>4? (h) What is the probability that sqrt(X)>2?
33.-
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6. Suppose you walk a hiking trail at a speed which is uniformly distributed from 4 to 6 miles per hour. The distance of the trail is 24 miles. Find the PDF of the duration of the trip. (Note: speed = distance/time)

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1. Find the density of Y = 1- e-ax when X ~ Exp(X). Note that the density of X is if r > 0, , otherwise. de-dz f(x) = { What is the name of the distribution of Y?