Question

please answer all parts for the first questions and only the last part for the second one. I posted the second one already but the the last part was incorrect. thank you for the help.

16. 0/0.35 points Previous Answers DevoreStat9 5.E.009. My Noteso Ask Your Teacher Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf xs 30, 20 s ys 30 20 fx,y) 0 otherwise (a) What is the value of K? (Enter your answer as a fraction.) 3/261632 K (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20 xs 30 and Y indeper (e) Are rv's? Yes, fx,y) fx(x) fy(y), so X and Y are independent Yes, fx,y)fx(x) . fyty), so X and Yare independent No, fx,y)fx(x) - fyy), so X and Y are not independent No, fx,y) fx(x) fyly), so X and Y are not independent. Need Help? Tak to a Tutor Read It Submit Answer Save Progress Practice Another Version 9 0.27/0.31 points Previous Answers DevoreStat9 4.E.028. My Notes Ask Your Teach Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) 0.4875 P(O sZs 2.24) (b) P(OsZ s 1) 0.3413 (c) 0.4861 P-2.20 s Z s 0) P-2.20 Z 2.20) (d) 0.9722 PIZ 1.82) (e) 0.9656 (f) 0.8749 P-1.15 Z) P-1.20 Z 2.00) (g) 0.8621 (h) P(1.82 Z 2.50) 0.0282 (i) P(1.20 s Z) 0.1151 (j) PIZ 2.50) 0.9938 You may need to use the appropriate table in the Appendix of Tables to answer this question

Answer 1

16a)

k=3/380000

b)

P(X<=26, Y<=26) =0.3024

c)

P(|X-Y|<=2) =0.3593

d)

f(x) =(1/20+3x²/38000)

e)

no f(x,y) $\neq$ f(x)*f(y) , so x and y are not independent