Hi everybody, I'm new so don't be harsh also I'm not a native speaker
I'm stuck with an exercise from my statistics class. I hope someone will take a few moments to have a look at it:
Problem 2 (Exponential Distribution)
Consider the random variable X with density
. . . . .\(\displaystyle f(x)\, =\, \begin{cases}0&x\, <\, 0\\c\, \cdot\, \mbox{exp}(-\lambda x)&x\, \geq\, 0 \end{cases}\)
with \(\displaystyle \, \lambda\, >\, 0.\)
(a) Determine c such that X is a random variable (two properties have to be fulfilled).
(b) Determine the associated cumulative distribution function (cdf) F (x).
in a) I determined that c > 0 and c must be a real number
in b) I know I have to integrate f(x) to get F(x)s, with the bound of integration -∞ and x
so I integrated by substitution and got the antiderivative -(ce-λx)/λ
now I have to insert x and -∞ and subtract the latter..
so when I insert x I get the antiderivative that I mentioned above but what happens when I insert -∞ is that the whole thing is going towards -∞ and this kind of doesn't make sense to me
I would be really glad if someone could tell me what I did wrong or how I can write this function down on my exercise sheet.. (I really need this point)
Thanks a lot in advance!
biomensch
I'm stuck with an exercise from my statistics class. I hope someone will take a few moments to have a look at it:
Problem 2 (Exponential Distribution)
Consider the random variable X with density
. . . . .\(\displaystyle f(x)\, =\, \begin{cases}0&x\, <\, 0\\c\, \cdot\, \mbox{exp}(-\lambda x)&x\, \geq\, 0 \end{cases}\)
with \(\displaystyle \, \lambda\, >\, 0.\)
(a) Determine c such that X is a random variable (two properties have to be fulfilled).
(b) Determine the associated cumulative distribution function (cdf) F (x).
in a) I determined that c > 0 and c must be a real number
in b) I know I have to integrate f(x) to get F(x)s, with the bound of integration -∞ and x
so I integrated by substitution and got the antiderivative -(ce-λx)/λ
now I have to insert x and -∞ and subtract the latter..
so when I insert x I get the antiderivative that I mentioned above but what happens when I insert -∞ is that the whole thing is going towards -∞ and this kind of doesn't make sense to me
I would be really glad if someone could tell me what I did wrong or how I can write this function down on my exercise sheet.. (I really need this point)
Thanks a lot in advance!
biomensch
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