probability density

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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(✰✰✰✰) (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.)
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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