Suppose that the probability of making a mistake in translation at each translational step is a small number, δ. Show that the probability, p, that a given protein molecule, containing n residues, will be completely error-free is (1 – δ)n.
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Suppose that the
The probability of making a mistake in a step is given as,
Then according to the property of complementary events,
Assuming that the translation of each step is an independent step.
Note that the probability of multiple independent events occurring simultaneously is equal to the product of each event occurring individually.
Step by step
Solved in 2 steps
- In the simple regression model (5.16), under the first four Gauss-Markov assumptions, we showed tha estimators of the form (5.17) are consistent for the slope, B1. Given such an estimator, define an esti mator of , by Bo = ỹ - BiT. Show that plim o = Bo-A research center claims that 24% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 26% say that they would travel into space on a commercial flight if they could afford it. At α=0.01, is there enough evidence to reject the research center's claim? Identify the claim and state H0 and Ha.Consider the spreading of Covid-19 in a company of 200 employees. 10 % of the employees have comorbidities and are more likely to have severe illness from Covid-19. Assume the virus spreads only during work lunch breaks and the increase in the number of employees infected is proportional to the current number of employees infected and also proportional to the current number of employees without Covid-19. Let an be the number of employees infected after n lunch breaks. Letk be the proportionality constant. Which is the following equations is a possible model for the above scenario? an-1= an + kan (20 - a,) an-1=an + kan-1 (200- a-1) an-1 = an + ka- an-1 ka, (20- an) None of the above
- A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=4,Y=3). Determine fxy(X=3,Y=4). Determine fxy(X=4,Y=4).3. 3 jobs, with i.i.d. runtimes each U[0, 1], are to be run in parallel on 2 processors. By how much time does the expected flowtime decrease if the schedule is changed from a best fixed schedule to a best schedule with recourse?Let {e} be a zero-mean, unit-variance white noise process. Consider a process {Y} which starts at time t = 0, and is defined recursively as follows: Let Yo = cieo, Y₁ = c₂Yo + e₁, and Y₁ = ¢₁Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process). a) Show that the process has zero mean. 1 b) For values of 01, 02 in the stationarity region for an AR (2) process, show how to choose C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that of a stationary AR(2) process with parameters 01, 02. c) Once the process {Y} has been generated, show how one can transform in into a new process which has any desired mean and variance. (Remark. This gives a method for simu- lating stationary AR(2) processes.)
- A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At a = 0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H, and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. O B. % of adults in the country would travel into space on a commercial flight if they could afford it. %. O C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not O D. No more than % of adults in the country would…An experiment is conducted to study the energy requirements of three physical activities: running, walking and cycling. Eight subjects are selected at random. It is thought that metabolic differences among the subjects might affect the kilocalories required for a given activity, hence, the experiment is done by taking into account of these differences. Each subject is asked to run, walk and cycle a measured distance, and the kilocalories expended per kilometre is determined for each subject during cach activity. The activities are run in a random order with time for recovery between activities. Subject Running Walking Cycling 0.7 1 1.4 1.1 2 1.5 1.2 0.8 3 1.3 1.3 0.7 0.8 1.8 4 1.7 0.7 0.1 5 6 1.6 1.5 1.2 0.7 0.4 0.6 7 1.7 1.1 8 2.0 1.3 a) State a statistical model and its assumptions. b) By using an ANOVA test, interpret whether there are differences in energy requirements for the three activities. Use a = 0.05. c) By using an ANOVA test, interpret whether there are differences in…Suppose that Y = Bo + BıXite, i - 1,..., n where E(€;) = 0 and Var(e;) = o². Let 3o and 3₁ be the least squares estimates. (a) Find Var(Bo) (treating the X's as fixed). (b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. i=1 (c) Show that ₁ ê¡¿Ÿ¿ = 0. What is the interpretation of this result? (d) Suppose you did a regression of Y's on the observed residuals. (In other words, treat the ê¿ as the X;'s.) What intercept and slope would you get?
- Suppose we take a random sample of size 25 form Bi(10, p). Find the pmf and the CDF of the 5th order statistic Y3.A researcher selected a sample of 268 former student-athletes from a list of graduates of a large university. A total of 14% of the sample of athletes had earned graduate degrees as compared to 17% of all graduates. What is the Z obtained value?
