Probability Density Function

[David Schopmeyer]

Let X be a continuous random variable with probability density function.

a. Find C
b. If X represents the time (in hours) that a certain substance can survive in a tropical region, find the probability that a randomly selected sample of the substance fails to outlive one that survives for 5 hours.

I have no clue where to start or how to do this problem...
Plz help!!

 

[Deleted member 4993]

Let X be a continuous random variable with probability density function.
View attachment 20053
a. Find C
b. If X represents the time (in hours) that a certain substance can survive in a tropical region, find the probability that a randomly selected sample of the substance fails to outlive one that survives for 5 hours.

I have no clue where to start or how to do this problem...Plz help!!

Tell us some of the properties of the probability-density-function.

Please show us what you have tried and exactly where you are stuck.​

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[HallsofIvy]

If you "have no clue where to start or how to do this problem" where did you get it? I would have thought this was a homework problem for a beginning "Probability and Statistics Class" but if you are taking such a class you surely should have learned what a "probability density function" is!

The integral of the "probability density function", to "x" gives the "probability distribution function" and one of the basic properties of probability is that its value is always from 0 to 1 and that the total of all probabilities is 1. That is, the integral of the probability density, over all possible values of x, is equal to 1. What is the integral of \(\displaystyle \frac{c}{3}xe^{-x}\) from 2 to \(\displaystyle \infty\)? What value of x will make that 1?

(I recommend "integration by parts".)

 

[yoscar04]

If you "have no clue where to start or how to do this problem" where did you get it? I would have thought this was a homework problem for a beginning "Probability and Statistics Class" but if you are taking such a class you surely should have learned what a "probability density function" is!

The integral of the "probability density function", to "x" gives the "probability distribution function" and one of the basic properties of probability is that its value is always from 0 to 1 and that the total of all probabilities is 1. That is, the integral of the probability density, over all possible values of x, is equal to 1. What is the integral of \(\displaystyle \frac{c}{3}xe^{-x}\) from 2 to \(\displaystyle \infty\)? What value of x will make that 1?

(I recommend "integration by parts".)

Small typo, I think you meant what value of c will make the integral =1.