Purchase Solution

Random Variables : Continuous R.V., Exponenetial, R.V, Mean and Variance

Not what you're looking for?

Ask Custom Question

3) Let X be a continuous random variable with probability density function
f(s)= c(1 + s^2) for -2 <= s <= 2.
a) Determine c
b) Determine Pr {X <= 0}
c) Determine the mean of X
d) Why is the previous answer fairly obvious?
e) Determine the variance of X
f) Compute Pr {X = 2 | X = 0}
g) Determine the cumulative distribution function

4) Let Y be an exponential random variable with parameter 1.5
a) Compute Pr {Y=0}
b) Compute Pr {Y > 2}
c) Compute Pr {Y > 4 | Y > 2}
d) Compute Pr {Y > 5 | Y > 3}
e) Compute Pr {Y > 5.6 | Y > 3.6}
f) Compute Pr {Y > x + 2 | Y > x } for x >= 0?
g) What is E[Y]?
h) What is the variance of Y

Purchase this Solution

Solution Summary

A cumulative distribution functions is calculated from a random variables and probability density function. Variance is calculated from an exponenetial random variable.

Solution Preview

Hi,
This is a pretty big assignment. I'll give you a method for solving each part, and leave the number crunching up to you.

3)
a)Recall that if you integrate the probability density function over the whole domain, you have to get 1. In this case the domain of f(s) is [-2, 2], so integrate f(s)ds from -2 to 2, let the result equal 1, and solve for the constant c. (I get c = 1/(4+16/3) which you can ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.