Random Variable Question [stuck]

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jasmeetcolumbia98

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Suppose that the random variable ? follows an exponential distribution with random (rate) parameter ?; where ? is uniformly distributed in the interval (?,?) with ? > ? > 0. Determine the mean and variance of ?.
I'm not sure where to start
 
jasmeetcolumbia98 said:
Suppose that the random variable ? follows an exponential distribution with random (rate) parameter ?; where ? is uniformly distributed in the interval (?,?) with ? > ? > 0. Determine the mean and variance of ?.
I'm not sure where to start
Click to expand...
Please give us the definition of - from your textbook or classnotes :

random variable​
​
exponential distribution​
​
Random rate parameter​

How is random parameter used in exponential distribution?
 
Subhotosh Khan said:
Please give us the definition of - from your textbook or classnotes :

random variable​
​
exponential distribution​
​
Random rate parameter​

How is random parameter used in exponential distribution?
Click to expand...
random variable - a variable whose value is unknown or a function that assigns values to each of an experiments outcomes.

exponential distribution - a continuous probability distribution

Random rate parameter - how often on average a given event could occur

Something like λ > 0 could be the rate parameter of a distribution. If a distribution has the interval [0, ∞), the random variable X has this distribution we'd write something like X ~ Exp(λ)
 
exponential distribution - a continuous probability distribution
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This is NOT a definition! Certainly an exponential distribution IS "a continuous probability distribution" but there are many "continuous probability distributions" that are NOT exponential distributions. What is the definition of "exponential distribution"?
 
HallsofIvy said:
This is NOT a definition! Certainly an exponential distribution IS "a continuous probability distribution" but there are many "continuous probability distributions" that are NOT exponential distributions. What is the definition of "exponential distribution"?
Click to expand...
it's also a probability distribution of the time between events in a Poisson point process
 
Are you saying that you do not know what an "exponential distribution" is? You really need to know the definition to do the problem you have posed!

Wikipedia, Exponential distribution - Wikipedia, gives the definition as \(\displaystyle P(x,\lambda)= \lambda e^{-\lambda x}\) for x greater than or equal to 0 and \(\displaystyle \lambda\) positive.
 
You are told that V is randomly distributed with probability distribution \(\displaystyle P(x)= Ue^{-Ux} \) and are asked to find the "mean"and "variance". Do you know what those mean?

This is very strange! You ask a question about an "exponential distribution" but don't seem to know what that is! Now you ask about the "mean" and "variance". Did you not look at the website I linked to? Those are given on that website.
 
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