Answer to Question #65296 in Statistics and Probability for shweta

Question

Which of the following statements are true or false? Give reasons for your answers. i) If X has the distribution )9,10(N and if 3X5Y−=, then Y has distribution )84,53(N. ii) If 7.0)BA(P,4.0)A(P=∪= and A and B are independent sets, then 55.0)B(P=. iii) By Chebyschev’s inequality, 2.0}2|x|{P≤σ≥μ−. iv) If correlation coefficient between x and y is 62.0, then correlation coefficient between u and v will by 62.0, where x65u+= and y37v−=. v) If UTθ=, where θ is an unknown parameter and U is a random variable having a chi-square distribution with n degrees of freedom (n being known), then an unbiased estimator of θ is T/2n