-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.

Given: We need to determine how much information about the signal's presence at the input we can…

Answered: are & and a 1 The probabilities for a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
A class contains 40 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.04. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF
The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.65, the probability that a car brought into the shop requires brake repair is 0.35, and the probability that a car requires both an oil change and brake repair is 0.24. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair. The probability that the car requires an oil change or brake repair is (Type an integer or a decimal.)
Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.
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?
a.2/9 b.2/3 c.1/3 d.1/9 e.3/8
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).
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?

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