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A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k .
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A random variable x has the following probability mass function f(x)=0...
Probability Mass Function
- A random variable x has the probability mass function:
- f(x) = 0 for x = 0
- f(x) = k for x = 1
- f(x) = 2k for x = 2
- f(x) = 2k for x = 3
- f(x) = 3k for x = 4
- f(x) = k^2 for x = 5
- f(x) = 2k^2 for x = 6
- f(x) = 7k^2 for x = 7
Calculating k
- We know that the sum of all probabilities in a probability mass function is 1.
- Therefore, we can set up the equation:
- 0 + k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 = 1
- Simplifying the equation:
- 13k^2 + 8k = 1
- Rearranging the terms:
- 13k^2 + 8k - 1 = 0
- Using the quadratic formula:
- k = (-b ± sqrt(b^2 - 4ac)) / 2a
- where a = 13, b = 8, and c = -1
- Plugging in the values and solving for k:
- k = (-8 ± sqrt(8^2 - 4(13)(-1))) / 2(13)
- k = (-8 ± sqrt(208)) / 26
- k = (-8 ± 4sqrt(13)) / 13
- Since k represents a probability, it must be greater than 0.
- Therefore, we take the positive value of k:
- k = (-8 + 4sqrt(13)) / 13
Conclusion
- The value of k is (-8 + 4sqrt(13)) / 13.
- A random variable x has the probability mass function:
- f(x) = 0 for x = 0
- f(x) = k for x = 1
- f(x) = 2k for x = 2
- f(x) = 2k for x = 3
- f(x) = 3k for x = 4
- f(x) = k^2 for x = 5
- f(x) = 2k^2 for x = 6
- f(x) = 7k^2 for x = 7
Calculating k
- We know that the sum of all probabilities in a probability mass function is 1.
- Therefore, we can set up the equation:
- 0 + k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 = 1
- Simplifying the equation:
- 13k^2 + 8k = 1
- Rearranging the terms:
- 13k^2 + 8k - 1 = 0
- Using the quadratic formula:
- k = (-b ± sqrt(b^2 - 4ac)) / 2a
- where a = 13, b = 8, and c = -1
- Plugging in the values and solving for k:
- k = (-8 ± sqrt(8^2 - 4(13)(-1))) / 2(13)
- k = (-8 ± sqrt(208)) / 26
- k = (-8 ± 4sqrt(13)) / 13
- Since k represents a probability, it must be greater than 0.
- Therefore, we take the positive value of k:
- k = (-8 + 4sqrt(13)) / 13
Conclusion
- The value of k is (-8 + 4sqrt(13)) / 13.
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A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k .
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A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k ..
A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k ..
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A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k ., a detailed solution for A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . has been provided alongside types of A random variable x has the following probability mass function f(x)=0,x=0k,x=1 2k,x=2 2k,x=3 3k,x=4 k^2,x=5 2k^2,x=6 7k^2+k,x=7 find the value of k . theory, EduRev gives you an
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