# Question: A real number between 0 and l00 is randomly selected

A real number between 0 and l00 is randomly selected according to a uniform distribution and rounded off to the nearest integer. For example, 36.5001 is rounded off to 37; √3 is rounded off to 2; and 69.49 is rounded off to 69. Define a random variable to be X = (number selected)–(nearest integer).

(a) What is the domain of this random variable?

(b) Determine the PDF for X.

(c) Determine the mean square value of X.

(a) What is the domain of this random variable?

(b) Determine the PDF for X.

(c) Determine the mean square value of X.

## Relevant Questions

A Gaussian random variable with zero mean and variance σ2X is applied to a device that has only two possible outputs, 0 or 1. The output 0 occurs when the input is negative, and the output 1 occurs when the input is ...A pair of random variables has a joint PDF specified by (a) Find (X > 2, Y < 0). (b) Find Pr (0 < X < 2, | Y + 1| > 2. (c) Find Hint: Set up the appropriate double integral and then use the change of variables: u = x – ...For the discrete random variables whose joint PMF is described find the following conditional PMFs: (a) PM (m |N = 2); (b) PM (m |N ≥ 2); (c) PM (m |N ≠ 2). Prove the triangle inequality which states that Determine whether or not each of the following pairs of random variables are independent: (a) The random variables described in Exercise 5.6; (b) The random variables described in Exercise 5.7; (c) The random variables ...Post your question