Exponential distribution moment generating function to find the mean

In summary, The Exponential distribution moment generating function is a mathematical function used to find the moments of an Exponential distribution, such as the mean, variance, and other properties. To find the mean using this function, the first derivative is taken at t=0. It is closely related to the probability density function and can be used to calculate probabilities. It can also be used to find higher moments such as variance and skewness. The main difference between this function and others is that it only has one parameter, λ, representing the rate of exponential decay. Other moment generating functions may have multiple parameters for different distribution characteristics.
  • #1
Askhwhelp
86
0
With mean = 2 with exponential distribution

Calculate

E(200 + 5Y^2 + 4Y^3) = 432

E(200) = 200

E(5Y^2) = 5E(Y^2) = 5(8) = 40

E(4Y^3) = 4E(Y^3) = 4(48) = 192

E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8

E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48

is this right?
 
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  • #2
Please take a look of this
 

What is the Exponential distribution moment generating function?

The Exponential distribution moment generating function is a mathematical function that calculates the moments of an Exponential distribution. It is used to find the mean, variance, and other properties of the distribution.

How do you use the Exponential distribution moment generating function to find the mean?

To find the mean using the Exponential distribution moment generating function, you need to take the first derivative of the function at t=0. This will give you the expected value or mean of the Exponential distribution.

What is the relationship between the Exponential distribution moment generating function and the probability density function?

The Exponential distribution moment generating function and the probability density function are closely related. The moment generating function is the Laplace transform of the probability density function. This means that the moment generating function can be used to calculate the probabilities of different values of the Exponential distribution.

Can the Exponential distribution moment generating function be used to find higher moments?

Yes, the Exponential distribution moment generating function can be used to find higher moments such as the variance, skewness, and kurtosis. These moments can be calculated by taking the higher derivatives of the moment generating function.

How does the Exponential distribution moment generating function differ from other moment generating functions?

The Exponential distribution moment generating function differs from other moment generating functions in that it only has one parameter, λ, which represents the rate of the exponential decay. Other moment generating functions may have multiple parameters to represent different characteristics of the distribution.

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