anonymous
  • anonymous
I'm trying to find what the summation from 0 to infinity of ((e^-4)4^x)/4! converges to (trying to show it is a valid pdf). Any suggestions on how to approach this would be welcome.
Mathematics
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions.

anonymous
  • anonymous
I'm trying to find what the summation from 0 to infinity of ((e^-4)4^x)/4! converges to (trying to show it is a valid pdf). Any suggestions on how to approach this would be welcome.
Mathematics
chestercat
  • chestercat
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

Jhannybean
  • Jhannybean
\[\huge \sum_{0}^{\infty} \frac{4^x(e^{-4})}{4!}\] Is it this? haha
anonymous
  • anonymous
haha yes
jdoe0001
  • jdoe0001
hmmm dunno that one :(

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
does the sequence limit to zero?
amistre64
  • amistre64
e^(-4)/4! is just some constant value ...
anonymous
  • anonymous
I believe it does, since the factorial grows faster than the exponential
anonymous
  • anonymous
oh sorry it's over x!
amistre64
  • amistre64
4^x is the only thing that varies .. the constant factors out ...
anonymous
  • anonymous
you're right, without that it wouldn't converge
amistre64
  • amistre64
.... can you pic the question? avoids alot of error
anonymous
  • anonymous
will try, h/o
anonymous
  • anonymous
\[p(x) = \frac{e^{-4}4^x}{x!}\]
amistre64
  • amistre64
pdf, probability density function ...
anonymous
  • anonymous
yeah, pmf not pdf. sorry, the pic was coming out really grainy
anonymous
  • anonymous
\[x = 0,1,2,...\]
amistre64
  • amistre64
we want the sumto equal ...1?
anonymous
  • anonymous
yes
anonymous
  • anonymous
i know i can pull out the constant
amistre64
  • amistre64
then it behooves us to consider that 4^x/x! = e^(4)
amistre64
  • amistre64
sum of ...
amistre64
  • amistre64
do you recall the taylor series for e^x ?
anonymous
  • anonymous
i don't i can look it up, that may be the prod in the right direction i am looking for
amistre64
  • amistre64
its a thought, not sure how well it will turn out tho
anonymous
  • anonymous
ah, yes. that looks like it exactly
anonymous
  • anonymous
\[e^x = \sum \frac{x^n}{n!}\]
amistre64
  • amistre64
im so clever it scares me ....
anonymous
  • anonymous
haha i liked how you looked at it in terms of solving for what would give us e^4
anonymous
  • anonymous
i appreciate the help
amistre64
  • amistre64
youre welcome :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.