stats_ps6_winter24

Stats Problem Set #6 1. Consider the joint probability distribution of X and Y : x = 4 x = 50 y = 1 0.3 0.2 y = 2 0.1 0.4 What is E ( X | y = 2) (rounded to four decimal places)? 2. Consider the joint probability distribution of X and Y : x = 2 x = 60 y = 6 0.3 0.2 y = 90 0.1 0.4 What is E ( Y | x = 2) (rounded to four decimal places)? 3. 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: n 0 1 2 P ( n ) 0.2 0.2 0.6 The number of word ( W ) errors is a random variable that has the following distribution: w 0 1 2 P ( w ) 0.2 0.4 0.4 Suppose the correlation between non-word errors and word errors is 0.2. What is ࠵? ࠵?+࠵? 2 (rounded to four decimal places)? - - + 50(8) = 10 8 o 6C] + 90% ) = 27 1 . 4396 NW = 0 . 64 + 0 56 + 220 . 2 t To . d = 1 . 52

4. 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: n 0 1 2 P ( n ) 0.3 0.1 0.6 The number of word ( W ) errors is a random variable that has the following distribution: w 0 1 2 P ( w ) 0.5 0.1 0.4 Suppose the correlation between non-word errors and word errors is 0.4. What is ࠵? ࠵?+࠵? (rounded to four decimal places)?

7) Consider the following information about random variables X , Y , A , and B : μ X = 3 σ X = 2 μ Y = 6 σ Y = 10 A = 0.8 X + 0.2 Y B = 0.6 X – 0.4 Y Suppose that ρ XY = 0.1. What is ࠵? ࠵? ? Round your final answer to four decimal places if necessary. 8) Consider the following information about random variables X , Y , A , and B : μ X = 4 σ X = 8 μ Y = 9 σ Y = 20 A = 0.9 X + 0.1 Y B = 0.7 X – 0.3 Y Suppose that ρ XY = 0.2. What is ࠵? ࠵? ? Round your final answer to four decimal places if necessary.

9. X and Y are two discrete random variables. If the covariance between X and Y is negative, then: ࠵? ࠵?+࠵? 2 _____࠵? ࠵? 2 + ࠵? ࠵? 2 . A) < B) > 10. Consider the joint probability distribution of X and Y : x = 0 x = 1 P ( y ) y = 0 0.2 0.1 0.3 y = 2 0.3 0.4 0.7 P ( x ) 0.5 0.5 1 What is ρ XY (rounded to four decimal places)?