For a binary communication system, find which input is more probable given that the receiver has output a 1. Assume that, a priori, the input is equally likely to be 0 or 1 and the probability of error from 0 to 1 is 0.2 and from 1 to 0 is 0.4.
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- Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the probability of transmitting a 4-bit code word with (a) at most one error, and (b) exactly four errors.A polling organization has been hired to conduct a survey to determine the proportion of people who are likely to support an upcoming ballot initiative. To help determine the size of the sample required for the main poll, a preliminary poll of 20 people is taken that yields the results below. (Yes indicates that the person will support the initiative, No indicates that they won't.) YesYesNoNoNoYesYesYesYesYesYesNoNoYesYesNoYesYesNoNoYesNoYesNoYesYesYesYesYesYesNoYesYesYesNoNoYesNoNoNo Based on the results of the peliminary poll, how large a sample is required for the main poll, assuming that the main poll should have a margin of error of 3% and a confidence level of 97.8%. Sample Size =Apply Big-M Method to the problem below and construct the initialtableau only.
- The lifespan X (years) of a species of pig has pdff (x) = 3x2e−x^3 , 0 < x < ∞.What is the probability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditionalprobability that it will live for at least another year?Supply the details for the proof of the Weierstrass M-TestAs a generalization of Example 5.3(figure), consider a test of n circuits such that each circuit is acceptable with probability p, independent of the outcome of any other test. Show that the joint PMF of X, the number of acceptable circuits, and Y, the number of acceptable circuits found before observing the first reject, is PX,Y(x,y) = ((n-y-1)C(x-y))*p^(x)*(1-p)^(n-x) For 0 ≤ y ≤ x < n p^(n) For x=y=n 0 otherwise Hint: For 0 ≤ y ≤ x < n, show that {X = x, Y = y} = A ∩ B ∩ C, where A: The first y tests are acceptable. B: Test y + 1 is a rejection. C: The remaining n − y − 1 tests yield x − y acceptable circuits
- If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. a) unlikely to have b) very unlikely to have c) guaranteed to have d) guaranteed to not havePlease Solve Subdivision d),e) and f) onlyA salesperson goes door-to-door in a residential area to demonstrate the useof a new household appliance to potential customers. At the end of a demonstration,the probability that the potential customer would place an order for the product is aconstant 0.2107. To perform satisfactorily on the job, the salesperson needs at leastfour orders. Assume that each demonstration is a Bernoulli trial. a) If the salesperson makes 15 demonstrations, what is the probability thatthere would be exactly 4 orders? b) If the salesperson makes 16 demonstrations, what is the probability thatthere would be at most 4 orders? c) If the salesperson makes 17 demonstrations, what is the probability thatthere would be at least 4 orders? d) If the salesperson makes 18 demonstrations, what is the probability thatthere would be anywhere from 4 to 8 (both inclusive) orders? e) If the salesperson wants to be at least 90% confident of getting at least4 orders, at least how…Please use Bayes' Theorem and show the prior, posterior, and the prior and posterior solution. Consider the dreaded disease Dipsidoodleitis. There are actually two forms of the disease, Type I and Type II, with the latter being more severe. Dipsidoodleitis is detected by a blood test. Values for people without dipsidoodleitis are normally distributed, M=70, sd=10. Values for people with Type I and Type II are distributed with M=80, sd=14, and M=110, sd=20, respectively. If a patient has a value of 90, what are the probabilities that she is dipsidoodleitis free, has the Type I version, or has the Type II version
- in a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment when considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60) (0.80)=0.48. is this student correct in his approach?A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?A new warehouse is being designed and a decision concerning the number of loading docks is required. There are two models based on truckarrival assumptions for the use of this warehouse, given that loading a truck requires 1 hour. Using the first model, we assume that the warehouse could be serviced by one of the many thousands of independent truckers who arrive randomly to obtain a load for delivery. It is known that, on average, 1 of these trucks would arrive each hour. For the second model, assume that the company hires a fleet of 10 trucks that are assigned full time to shipments from this warehouse. Under that assumption the trucks would arrive randomly, but the probability of any truck arriving during a given hour is 0.1. Obtain the appropriate probability distribution for each of these assumptions and compare the results.