Answer all questions by 11:59 pm CST 5/7/21

1. Consider the joint probability distribution of X and Y: What is E(le = l) (rounded to four decimal places)? Consider the joint probability distribution of X and Y: What is E(le = 60) (rounded to four decimal places)? Undergraduates are asked to write a SOD-word essay. The number of non-word (N) errors is a random variable that has the following distribution: 2 P00 0.8 The number of word (W) errors is a random variable that has the following distribution: -_-__ 2 -z_-_ 0.5 Suppose the correlation between non-word errors and word errors is 0.5. What is the mean of the total number of errors (umw) (rounded to four decimal places J? Undergraduates are asked to write a 300-word essay. The number of non-word (N) errors is a random variable that has the following distribution: 2 0.8 P0!) The number of word (W) errors is a random variable that has the following distribution: w 0 l 2 P(w) 0.1 0.4 05 Suppose the correlation between non-word errors and word errors is 0.5. What is the standard deviation of the total number of errors (Omar) (rounded to four decimal places}? 5. Consider the joint probability distribution of X and Y: x =0 x=1 y= 0 0.1 0.4 y=1 0.1 0.4 In this example, X and Y are In this example, X and Y are A) independent, correlated B) independent, uncorrelated C) not independent, correlated D) not independent, uncorrelated 6. Consider the joint probability distribution of X and Y: x =0 x=1 y = 0 0.2 0.2 y=1 0.1 0.5 In this example, X and Y are In this example, X and Y are A) independent, correlated B) independent, uncorrelated C) not independent, correlated D) not independent, uncorrelated7) Consider the following information about random variables X , Y, A, and B: mm- A=0.8X+02Y B=0.&X 0.4? Suppose that my = 0.2. What is 0'3? Round your nal answer to four decimal places if necessary. 8) Consider the following information about random variables X, Y, A, and B: m-M-nm A=0.9X+0-1Y B=0.7X 0.3Y Suppose that pxy = 0.5. What is 0);? Round your nal answer to four decimal places if necessary. A) B) 10. X and Yare two discrete random variables. If the covariance between X and Y is positive, then: U+y_0' + 0%. Consider the joint probability distribution of X and Y: What is my (rounded to four decimal places