# Question: A random variable has the following exponential PDF Where and are

A random variable has the following exponential PDF:

Where and are constants.

Determine the required relationship between a and b.

Determine the corresponding CDF.

Where and are constants.

Determine the required relationship between a and b.

Determine the corresponding CDF.

## Relevant Questions

A certain random variable has a probability density function of the form f x (x) = ce –2xu(x). Find the following: (a) The constant c, (b) Pr (X >2), (c) Pr (X < 3), (d) Pr (X < 3|X > 2). Find the value of the constant that makes each of the following functions a properly normalized PDF. (a) (b) (c) (d) Suppose we measure the noise in a resistor (with no applied voltage) and find that the noise voltage exceeds 10 µV 5% of the time. We have reason to believe the noise is well modeled as a Gaussian random variable, and ...Let be a Rayleigh random variable whose PDF is fa (r) = crexp (0-r2) u (r). (a) Find the value of the constant c. (b) Find Pr (R >r) for an arbitrary constant r. (c) Find Pr (R > 1 | R < 2). Suppose we flip a balanced coin five times and let the random variable represent the number of times heads occurs. (a) Sketch the CDF of X fx (x). (b) Write fx (x), analytically in terms of unit step functions.Post your question