Daniel Bernoulli's work in 1760 had the goal of appraising the effectiveness of a controversial inoculation program against smallpox, which at that time was a major threat to public health.Question 1. Who was Daniel Bernoulli?Why was he working on this project?Bernoulli's model applies equally well to any other disease that, once contracted and survived, confers a lifetime immunity.Consider the cohort of individuals born in a given year𝑡=0t=0, and let𝑛(𝑡)n(t) be the number of these individuals surviving 𝑡t years later.Let 𝑥(𝑡)x(t)be the number of members of this cohort who have not had smallpox by year 𝑡t and who are therefore still susceptible. Let 𝛽β be the rate at which susceptibles contract smallpox, and let 𝜈ν be the rate at which people who contract smallpox die from the disease. Finally, let 𝜇(𝑡)μ(t) be the death rate from all causes other than smallpox. Then 𝑑𝑥𝑑𝑡dxdt, the rate at which the number of susceptibles declines, is given by𝑑𝑥𝑑𝑡=−[𝛽+𝜇(𝑡)]𝑥dxdt=−[β+μ(t)]x (1)The first term on the right of Eq.1 is the rate at which susceptibles contract smallpox, and the second term is the rate at which they die from all other causes. Also,𝑑𝑛𝑑𝑡=−𝜈𝛽𝑥−𝜇(𝑡)𝑛dndt=−νβx−μ(t)n, (2)where 𝑑𝑛𝑑𝑡dndt is the death rate of the entire cohort, and the two terms on the right side are the death rates due to smallpox and to all other causes, respectively.Introduce a new variable 𝑧(𝑡)=𝑥(𝑡)𝑛(𝑡).z(t)=x(t)n(t).Question 2.Formulatetheinitial value problem for 𝑧(𝑡)z(t).Question 3. Find the complete general solution to differential equation in Q.2 equation.Question 4. Find the solution to the initial value problem.Question 5. Draw the slope field( by hand, or with DField oruse MATLAB, for example, ode45) for this equation and draw some representative solutions. What does this picture tell youabout the solution to this initial value problem.Question 6.Does the solutionin Q.5 agree with your analysis in Q. 4?Question 5. Bernoulli estimated that 𝜈=𝛽=1/8ν=β=1/8.With that in mind, determine the proportion of 20-year-olds who have not had smallpox.On the basis of the model just described and the best mortality data available at the time, Bernoulli calculated that if deaths due to smallpox could be eliminated, 𝜈=0ν=0, then the life expectancy among inoculated will increase by almost 10%.Question 6. Check the internet for the information about what was the life expectancy in 1760 in the country where Bernoulli lived. How would the inoculation program change it?As a result of this study,Bernoullisupported the inoculation program.

With this database, you will:Identify and list categorical and continuous variables.Calculate frequencies and percentages for all of the categorical variables, and means, and standard deviations for the continuous variables.Run a one-sample z test of proportions for one categorical variable. Here is an example in terms of wording: "Is the proportion of English speaking patients greater than 50%?" Using .05 level of significant test the appropriate hypotheses.Write the null and alternate hypothesesWhat is the proportion of English speaking patientsWhat is the standard error and z statisticsFind critical z and p value. Is the p value significant? Conclusion?Run an independent samples t-test to compare two groups of people (specified by a dichotomous variable) on one continuous variable. Using .05 level of significant test the appropriate hypotheses. In order to run this test statistics you have to re-arrange your data.Write the null and alternate hypotheses.What is the calculated mean for each group?What is the confidence interval for each group?What is the critical t value?Is the p value significant? Conclusion?I DONT UNDERSTAND ANYTHING CAN SOMEONE PLEASE HELP