Purchase Solution

# Distribution Theory

Not what you're looking for?

Determine the distribution of Y = X_1 + X_2 + . . . + X_n
by first determining the joint distribution of

Z_1 = X_1
Z_2 = X_1 + X_2
Z_3 = X_1 + X_2 + X_3
.
.
.
Z_n = X_1 + X_2 + X_3 + . . . + X_n

and then computing the marginal distribution of Z_n

According to my text book:

Exp(a), a>0 has density

f(x)=(1/a)e^(-x/a), x>0

and E[X]=a Var(X)=a^2 and the characteristic function is phi x(t)=1/(1-ait)

This is all the information I have regarding this problem. I hope its enough for someone. I have no idea what to do with this and I need a detailed step by step answer if possible. I really need help on this please!!! I have a test on Tuesday!!

##### Solution Summary

The solution describes the determination of the joint distribution of the sum of n independent Exponential random variables.

##### Solution Preview

Here it is given that are independent Exp[a] distributed random variables.
Now, the probability density function of is given by,

Thus the joint probability density function of is given ...

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

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

##### Exponential Expressions

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