vinodbhati5576

1. [5 pts) Let Yı, Y2, and Y3 be three independent random variables such that each Y, i = 1,2,3, has a Rayleigh distribution with parameter B. Let the random variable X be defined as X = Y? + Y3 + Y3. Find the probability density function of X.

Let X1, X2, and X3 be three independent gamma random variables with parameters (, 2), (3, 2), (, 2) respectively. Use the joint distribution of functions of random variables and the Jacobian to show that Y1 = and Y2 = X1+ X2 are independent and that Y2 ~ I'(, 2). Conclude by reasoning that and го Хз are independent. r1trg

3. Let Y.Y,...,Y be independent random variables with Binomial distribution with parameters: (number of trails) ni, 12,...,nk respectively, and the same p (probability of success in trials). Derive the probability distribution of U = Y1 + Y2 + ... +Yk.

Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter " " defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given. Suppose you are now in a different reality, in which this binomial probability parameter is now unknown to you but you are still interested in carrying out the original study described above, though you must first estimate with a certain level of confidence. Furthermore, you would also like to collect data from adults to examine the difference between the proportion with nausea and vomiting following holiday parties of schoolchildren and adults, which will reflect any possible age differences in becoming sick. You obtain research funding to randomly sample 31 schoolchildren and 45 adults with an inclusion criterion that a given participant must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician and general practitioner for the schoolchildren and adults, respectively. After anxiously awaiting your medical colleagues to complete their medical assessments, they email you data contained in the following tables. Table 1. Schoolchildren Table 2. Adults What is the estimated 95% confidence interval (CI) of the difference in proportions between schoolchildren and adults developing nausea and vomiting following holiday parties? Assign groups 1 and 2 to be schoolchildren and adults, respectively. Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 3) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 4) you may copy and paste the data into Excel to facilitate analysis. Select one: a. -0.4983 to -0.1497 b. -0.5887 to -0.1506 c. -0.6298 to -0.1549 d. -0.5476 to -0.1721

Suppose at random, 44% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=29. What is the probability that between 9 and 29 children become sick?

In a large clinical​ trial,

children were randomly assigned to two groups. The treatment group consisted of

children given a vaccine for a certain​ disease, and

of those children developed the disease. The other

children were given a​ placebo, and

of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of

and

Consider the reaction below. What is the limiting reactant when 2.60 g of ethene (C2H4, molar mass = 28.0 g/mol) and 32.0 g of oxygen (molar mass = 32.0 g/mol) are reacted?C2H4(g) + 3O2(g) 2CO2(g) + 2H2O(g)