Consider a data set that has 15 observations on one variable, x:
x<-c(1,5,2,2,3,4,0,5,1,2,4,3,3,3,4,2) 1. Create a table in the style of table 4.3 in the lecture notes, showing x, f (x), and F(x). 2. Plot a histogram-type PMF for x. 3. Produce a table calculating the mean and standard deviation of x, similar in style totable 4.7 in the lecture notes. Table 0.1 below is the joint PMF of random variables X and Y. Table 0.1: Joint Distribution for X and Y Y 0 1 2 0 0.15 0.10 0.05 1 0.10 0.05 0.10 X 2 0.05 0.10 0.05 3 0.10 0.05 0.10 1 4. Calculate f (x), the marginal distribution of X, and the corresponding mean and variance by producing a table like Table 4.11 in the lecture notes. 5. Calculate f (x | y = 1), the conditional distribution of X, given y = 1, and the corresponding mean and variance by producing a table like Table 4.12 in the lecture notes.

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