19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.
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- A chemical system that results from a chemical reaction has two important components among others in a blend. The joint distribution describing the proportions X₁ and X₂ of these two components is given by (2, f(x1, x₂) = 10, 0 0.5? (d) Give the conditional distribution fx₁x₂ (112).Second part of c, as well as parts d and eCalculate the number based cumulative frequency distribution, Qn, and differential frequency distribution, qn, and tabulate values (showing units) at appropriate grid points xi. answers attached
- When do we use a mean and SD to define a continuous variable distribution?A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?Describe in words: 1. Marginal Distribution(Continuous Random Variables) 2. Marginal Distribution(Discrete Random Variables)
- Please selct all that apply and explain whyThe normal distribution is a family of distributions that is often used to model operational processes. Give one example of how the normal distribution can be used in an operations or production environment. Be sure to explain how the normal distribution is used in the example provided.How do you interpret the coefficients for the incomegrouplow and incomegroupmiddle in the photo? (please provide explanation)
- Curing times in days (x) and compressive strengths in MPa (V) were recorded for several concrete specimens. The means and standard deviations of the x and y values were * = 5, s, = 2, 5 = 1350, s, = 100. The correlation between curing time and compressive strength was computed to be r = 0.7. Find the equation of the least-squares line to predict compressive strength from curing time.Use ”margin.table” to get the Titanic marginal table for factors 1 (class of accomodations) and 4 (survival). Apply the chi-square test to see if class and survival are dependent. Do it both by hand and with ”chisq.test” in R. Attached is the data output from R-studio. Please apply the chi-aquare test on that by hand method ASAP needed. Thanks.Please do not give solution in image formate thanku. Define a conditional median of Y given X = x to be any median of the conditional distribution of Y given X = x. Suppose that we will get to observe X and then we will need to predict Y. Suppose that we wish to choose our prediction d(X) so as to minimize mean absolute error (MAE), E(|Y − d(X)|). Prove that d(x) should be chosen to be a conditional median of Y given X = x. You can use the fact that for a univariate random variable MAE is minimized at the median, m.