4. Let X equal the larger outcome when a pair of four-sided dice are rolled. Let D be the outcome space showing the paired outcomes of the two dice, with p = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4,2), (4,3), (4, 4)}. Assuming that the two dice are fair and independent, each of these outcomes has probability P({i, j}) = (a) Identify the outcome space of X, and its probability function f(x). (b) Find the mean of X. (c) The form of the probability function can be generalised to a pair of independent and fair m-sided dice, where X, the larger number shown, has probability function f(x) = 2x 1 m² x = 1,..., m. 2 Noting that ₁ = m(m+1)/2 and Σ² = m(m+1)(2m+1)/6, demon- strate that the probability function is valid, and confirm that the mean is (m+1)(4m-1) E(X) = 6m (d) Use the result in (c) to verify your answer in (b). NB: The first two parts are numerical. For the third part, you need not derive the formula for f(x), but rather check that it sums algebraically to the appropriate value. Use the definition of the mean of a discrete random variable, and seek to rearrange so that and can be exploited. The final part is computational.

4. Let X equal the larger outcome when a pair of four-sided dice are rolled. Let D be the outcome space showing the paired outcomes of the two dice, with p = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4,2), (4,3), (4, 4)}. Assuming that the two dice are fair and independent, each of these outcomes has probability P({i, j}) = (a) Identify the outcome space of X, and its probability function f(x). (b) Find the mean of X. (c) The form of the probability function can be generalised to a pair of independent and fair m-sided dice, where X, the larger number shown, has probability function f(x) = 2x 1 m² x = 1,..., m. 2 Noting that ₁ = m(m+1)/2 and Σ² = m(m+1)(2m+1)/6, demon- strate that the probability function is valid, and confirm that the mean is (m+1)(4m-1) E(X) = 6m (d) Use the result in (c) to verify your answer in (b). NB: The first two parts are numerical. For the third part, you need not derive the formula for f(x), but rather check that it sums algebraically to the appropriate value. Use the definition of the mean of a discrete random variable, and seek to rearrange so that and can be exploited. The final part is computational.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

its actually a
comp: /-
when you should use T test
Can someone help?
its not correct
Explain why A and -A always have the same reduced echelon form R.
I am still confused
Could you also look at the second page ?