probability density
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
Related questions
Question
![(✰✰✰✰) (a) Find the interval of values for q with the property that (for an appropriate constant K) a random variable with probability density
K₁
p(x) =
will have a well-defined mean but an undefined variance. Answer using interval notation, where () denotes an empty
(x² + 2x+122)
interval.
Answer: The interval described above is {}
(b) A certain random variable X has the probability density function p(x) =
K2
(x2+2x+122)21
Find the following:
K2=
E[X] =
Var[X] =
Hint: For any random variable X and constant k, one has
E[X − k] = E[X] − k
and Var[X-k] = Var[X].
(Proving this is a worthwhile exercise in itself.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06180921-9ba3-476d-9538-add8b79e3ee2%2Fdde5e02f-88a5-4089-bf91-63c7bb4c1a6a%2Fkk3rvcc_processed.png&w=3840&q=75)
Transcribed Image Text:(✰✰✰✰) (a) Find the interval of values for q with the property that (for an appropriate constant K) a random variable with probability density
K₁
p(x) =
will have a well-defined mean but an undefined variance. Answer using interval notation, where () denotes an empty
(x² + 2x+122)
interval.
Answer: The interval described above is {}
(b) A certain random variable X has the probability density function p(x) =
K2
(x2+2x+122)21
Find the following:
K2=
E[X] =
Var[X] =
Hint: For any random variable X and constant k, one has
E[X − k] = E[X] − k
and Var[X-k] = Var[X].
(Proving this is a worthwhile exercise in itself.)
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