**Understanding Hardy-Weinberg Equilibrium**Let $ A $ and $ B $ represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type $ A $ and 30% are type $ B $. The locus is said to be in Hardy-Weinberg equilibrium if the proportion of organisms that are of type $ AB $ is $(0.40)(0.30) = 0.12$.In a sample of 300 organisms, 42 are of type $ AB $. Can you conclude that this locus is not in Hardy-Weinberg equilibrium?**Analysis:**To determine if the locus is in Hardy-Weinberg equilibrium, we calculate the expected number of $ AB $ genotypes:1. **Expected Proportion**: Given the proportion $ (0.40)(0.30) = 0.12 $.2. **Expected Number**: For 300 organisms, expected $ AB $ = $ 300 \times 0.12 = 36 $.**Observation**: We have 42 $ AB $ in the sample.**Conclusion**: Compare the observed value (42) to the expected value (36). If the difference is significant, it suggests the locus might not be in Hardy-Weinberg equilibrium. Further statistical tests, like a chi-square test, can determine the significance of this difference.

Given 40% of the type A 30% of the type B AB = (0.40)(.30) = 0.12 In a sample of 300 Organisms. 42…

Answered: Let A and B represent two variants…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy-Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40)(0.30) = 0.12. In a sample of 300 organisms, 42 are of type AB. Can you conclude that this locus is not in Hardy-Weinberg equilibrium?
Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. dN Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) stable N = unstable N =
2. A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X = the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y = the proportion of the time that the walk-up window is in use. Then the set of possible values for (X, Y) is the rectangle D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}. Suppose the joint probability density function of (X, Y) is given by: fx,y(x,y) = { / (x + y ² ) ²²(x + y²) 0≤x≤ 1,0 ≤ y ≤ 1 Otherwise 0 (a) Show that fx,y is legitimate (b) Find the probability that neither facility is busy more than one-quarter of the time. (c) Find fx and fy, the marginal probability density function of X and Y respectively. (d) Construct the conditional probability density function of Y given that X=0.8. (e) Evaluate the probability that the walk-up facility is busy at most half of the time given that X=0.8 (f) Calculate the expected proportion of the time that the walk-up facility…
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5% QUESTION 17 In an MLR…
A building contains 1000 lightbulbs. Each bulb lasts at most five months. The company maintaining the building is trying to decide whether it is worthwhile to practice a “group replacement” policy. Under a group replacement policy, all bulbs are replaced every T months (where T is to be determined). Also, bulbs are replaced when they burn out. Assume that it costs $0.05 to replace each bulb during a group replacement and $0.20 to replace each burned-out bulb if it is replaced individually. How would you use simulation to determine whether a group replacement policy is worthwhile?
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = B, + B,x + E where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow (y) Vehicle Speed (x) 1,257 35 1,329 40 1,227 30 1,335 45 1,351 50 1,123 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ý = bo + b,x + b,x? (a) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.)
7B A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #1 contains the TBV of the normal patients and Table #2 contains the TBV of schizophrenia patients ("SOCR data Oct2009," 2013). Table #1: Total Brain Volume (in mm3) of Normal Patients 1663407 1583940 1299470 1535137 1431890 1578698 1453510 1650348 1288971 1366346 1326402 1503005 1474790 1317156 1441045 1463498 1650207 1523045 1441636 1432033 1420416 1480171 1360810 1410213 1574808 1502702 1203344 1319737 1688990 1292641 1512571 1635918 Table #2: Total Brain Volume (in mm3) of Schizophrenia Patients 1331777 1487886 1066075 1297327 1499983 1861991 1368378 1476891 1443775 1337827 1658258 1588132 1690182 1569413 1177002 1387893 1483763 1688950 1563593 1317885 1420249 1363859 1238979…
displays blood pressure status by gender. Blood Pressure by Gender Optimal Normal Hypertension TotalThe required value is, Male 22 73 55 150 Female 43 132 65 240 Total 65 205 120 390 What proportion of the participants has optimal blood pressure? What proportion of men has optimal blood pressure? What proportion of participants with hypertension are men? Are hypertensive status and male gender independent?

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