Mathematics Exam > Mathematics Questions > Distribution function is given as below 0 x i...
Start Learning for Free
Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?
?
?
Most Upvoted Answer
Distribution function is given as below 0 x is less than minus 1 1 by ...
Understanding the Distribution Function
The distribution function, often referred to as the cumulative distribution function (CDF), provides the probability that a random variable X will take a value less than or equal to x. Given your piecewise function, we can analyze it as follows:
Defined Intervals
- 0 for x < />
- 1/5 for -1 ≤ x < />
- 7/10 for 0 ≤ x < />
Determining the Probability Density Function (PDF)
The PDF is the derivative of the CDF. To find it, we will differentiate the cumulative probabilities defined over the intervals.
Steps to Find PDF
- For x < />
The CDF is constant (0), hence the PDF is 0.
- For -1 ≤ x < />
The CDF is 1/5, which is also constant. Thus, the PDF remains 0.
- For 0 ≤ x < />
The CDF is 7/10. Differentiating this constant value gives a PDF of 0.
Final PDF Formulation
Putting this all together, we can express the PDF as:
- f(x) = 0 for x < />
- f(x) = 0 for -1 ≤ x < />
- f(x) = 0 for 0 ≤ x < />
Conclusion
The PDF derived from the given CDF indicates that the random variable has no probability density in the specified intervals. This signifies that there are no outcomes in the defined ranges, leading to a uniform absence of probability density throughout the intervals analyzed.
The distribution function, often referred to as the cumulative distribution function (CDF), provides the probability that a random variable X will take a value less than or equal to x. Given your piecewise function, we can analyze it as follows:
Defined Intervals
- 0 for x < />
- 1/5 for -1 ≤ x < />
- 7/10 for 0 ≤ x < />
Determining the Probability Density Function (PDF)
The PDF is the derivative of the CDF. To find it, we will differentiate the cumulative probabilities defined over the intervals.
Steps to Find PDF
- For x < />
The CDF is constant (0), hence the PDF is 0.
- For -1 ≤ x < />
The CDF is 1/5, which is also constant. Thus, the PDF remains 0.
- For 0 ≤ x < />
The CDF is 7/10. Differentiating this constant value gives a PDF of 0.
Final PDF Formulation
Putting this all together, we can express the PDF as:
- f(x) = 0 for x < />
- f(x) = 0 for -1 ≤ x < />
- f(x) = 0 for 0 ≤ x < />
Conclusion
The PDF derived from the given CDF indicates that the random variable has no probability density in the specified intervals. This signifies that there are no outcomes in the defined ranges, leading to a uniform absence of probability density throughout the intervals analyzed.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Question Description
Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf??.
Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf??.
Solutions for Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? defined & explained in the simplest way possible. Besides giving the explanation of
Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf??, a detailed solution for Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? has been provided alongside types of Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? theory, EduRev gives you an
ample number of questions to practice Distribution function is given as below 0 x is less than minus 1 1 by 5 minus 1 less than equal to x less than0 7 by 10b 0 less than equal to x less 1 1 Find pdf?? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily