-The probabilities for a signal to be received or not receivedare & and a = 1 -a, respectively. As a result of noise, a signal entering thereceiver can be recorded at its output with probability 3 and not recordedwith probability 8 = 1-3. In the absence of the signal at the input, it can berecorded at the output (because of noise) with probability y and not recordedwith probability y = 1 - y. What quantity of information about the presenceof the signal at the input do we obtain by observing it at the output.

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Answered: - The probabilities for a signal to be…

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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The problem of traffic delay in a highway can be studied in the following way. Let us assume that the probability of no traffic delay in one period, given no traffic delay in previous period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the previous period is 0.75. The period of time is 30 minutes.
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
A certain disease has a prevalence of in a population. The rate of false 4 positives is 10% and and the rate of false negatives is 5%. If you are exposed to the disease, then probability that you contract it is . You can only contract the disease by sharing food. Suppose that you meet 10 people, that each person tests negative for the disease, and that you share food with each of them exactly three times. What is the probability that you contract the disease?
Q. 2 The probability that a smoker who consumes over 20 cigarettes a day will suffer from chronic respiratory illness is 4 The 10 probability that he will suffer from heart disease is The 10 probability that he will suffer from at least one of these ailments is 6.5 10 (i) Find the probability that the smoker will suffer from both ailments. (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness. (iii) Find the probability that he will suffer from chronic respiratory illness given that he suffers from heart disease. (iv) Are events "chronic respiratory illness" and "heart disease independent"?
The probability that a new computer functions for over 10,000 hours is 0.8, the probability that it functions for over 20,000 hours is 0.4 and the probability that it functions for over 30,000 hours is 0.1. If a new computer is still working after 10,000 hours, what is the probability that i. its total life will exceed 20,000 hours;ii. its additional life will exceed 20,000 hours?
Suppose the probability of getting the flu is 0.20, the probability of getting a flu shot is 0.60, and the probability of bothgetting the flu and a flu shot is 0.10. (a) Find the probability of the union between (getting the the flu) and (getting the flu shot).
Assume. that the probability that any child born in the population will be a boy is 0.51 and the probability that it will be a girl is 0.49. If a family has six children, what is the probability they will have 3 boys and 3 girls?
Q1. Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: What is the probability that at least one girl is born?
L Hz = 5. For the following performance function and values shown for the variables, determine the safety index (B) and probability of failure (P). Use the First Order Reliability Method (FORM) by applying the formulas below. Then use the standard normal table provided to find Pf. Z= f(w,x,y) = w³ x² + xy²-5 w²y Formulas: µz = f(µw, µx, Hy) Oz || mial formula to find the probabili W B= X y Mean (u) 3 2= Oz (OZ / Ow) 2 |μ (ow ²) + (OZ / Ox)² μ (ox ²) + (OZ / Oy)² μ (oy ²) B = μz / Oz Pf = 1 - F (B) 5 2 Std. dev. (o) 0.5 1 0.5 Pf= Enter

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