4. The cumulative distribution function of a continuous random variable, X is given as follows: x< 0 F(x)=- -x(x+4), 32 Osx<4 1 x24 (a) Calculate P(|X–1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).
4. The cumulative distribution function of a continuous random variable, X is given as follows: x< 0 F(x)=- -x(x+4), 32 Osx<4 1 x24 (a) Calculate P(|X–1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![4.
The cumulative distribution function of a continuous random variable, X is given
as follows:
x<0
F(x) =
- x(x+4),
32
0Sx<4
1
x24
(a)
Calculate P(|X-1|<1).
(b)
Find the median.
(c)
Determine the probability density function of X. Hence, evaluate
E(3X² -1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F058ec046-f684-4366-ba29-6b55124595b2%2Fc1ecf29b-3974-4c20-8f95-57b0c1de5c49%2Fogmnit_processed.png&w=3840&q=75)
Transcribed Image Text:4.
The cumulative distribution function of a continuous random variable, X is given
as follows:
x<0
F(x) =
- x(x+4),
32
0Sx<4
1
x24
(a)
Calculate P(|X-1|<1).
(b)
Find the median.
(c)
Determine the probability density function of X. Hence, evaluate
E(3X² -1).
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