The probability density function for the continuous random variable X is given by: (A(x² f (x) = - 2x + 21) 0

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The probability density function for the continuous random variable
X is given by:
(А(х* — 2х
- 2x + 21) 0 < x < 3
f (x) =
ЗА
3 <x < 4
otherwise
%3D
Where A is a constant
a) Find the value of A
b) Find the cumulative distribution function F(x).
c) Show that the median of X lies between x = 2.6 and x = 2.7.
%3D
d) Find the mean and standard deviation of X
e) Compute E (X + 2)².
Transcribed Image Text:The probability density function for the continuous random variable X is given by: (А(х* — 2х - 2x + 21) 0 < x < 3 f (x) = ЗА 3 <x < 4 otherwise %3D Where A is a constant a) Find the value of A b) Find the cumulative distribution function F(x). c) Show that the median of X lies between x = 2.6 and x = 2.7. %3D d) Find the mean and standard deviation of X e) Compute E (X + 2)².
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