Answer to Question #65580 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 N(9,10)and if Y=5x-3, then Y has distribution N(84,53)

Answer 1

The answer is false.

If X has a distribution N(m_1, s_1^2), Y has a distribution N(m_2, s_2^2) than (X + Y) has a distribution N(m_1 + m_2, s_1^2 + s2^2),
therefore Y = 5x - 3 will a distribution N(5 * 9 - 3, 5 * 10) = N(42, 50).