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The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)?
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The continuous random variable X is uniformly distributed with mean1 a...
Problem Statement
Given that the continuous random variable X is uniformly distributed with mean 1 and variance 3, find P(X > 0).
Solution
Let us first find the standard deviation of the random variable X.
- Given that variance of X is 3, we have Var(X) = 3
- Also, we know that the variance of a uniformly distributed random variable (with a and b as its limits) is given by:
Var(X) = (b - a)^2 / 12
- Substituting the values, we get:
3 = (b - a)^2 / 12
b - a = 2√3
Since the mean of X is 1, we have:
Mean(X) = (a + b) / 2 = 1
So, a + b = 2
Now, we can solve these two equations to get:
a = 1 - √3 and b = 1 + √3
Thus, the standard deviation of X is:
SD(X) = √Var(X) = √3
Now, we can calculate the required probability:
P(X > 0) = P(Z > (0 - 1) / √3) where Z is the standard normal random variable
= P(Z > -√3 / 3)
= P(Z < √3 / 3)
= 0.63 (from standard normal distribution table)
Conclusion
The probability that the continuous random variable X is greater than 0 is 0.63.
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The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)?
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The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)?.
The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The continuous random variable X is uniformly distributed with mean1 and variance 3, find P(X 0)?.
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