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Continuous Random Variables
When will that bus finally arrive? How hot is it going to be outside today? These any many other real-world values can be modeled by continuous random variables.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Let \(X\) and \(Y\) have the joint probability density function: \[f(x,y)=\frac{1}{49}xy\] for \(0\leq x\leq2\) and \(0\leq y\leq7.\) Find the expected value of \(3X.\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Let \(X\) and \(Y\) have the joint probability density function: \[f(x,y)=k(x+y)\] for \(0\leq x\leq10\) and \(0\leq y\leq1,\) where \(k\) is a constant. Find the marginal probability \(P(1\leq X\leq2).\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Let \(X\) and \(Y\) have the joint probability density function: \[f(x,y)=k\] for \(0\leq x\leq5\) and \(0\leq y\leq8,\) where \(k\) is a constant. Find the covariance between \(X\) and \(Y.\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Let \(X\) and \(Y\) have the joint probability density function: \[f(x,y)=kxy\] for \(0\leq x\leq4\) and \(0\leq y\leq3,\) where \(k\) is a constant. Find \(P(X>Y).\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Which of the following CANNOT be the joint probability density function of two continuous random variables \(X\) and \(Y?\)
(A): \(f(x,y)=1\) for \(0\leq x,y\leq1.\)
(B): \(f(x,y)=x+y\) for \(0\leq x,y\leq1.\)
(C): \(f(x,y)=xy\) for \(0\leq x,y\leq1.\)
(D): \(f(x,y)=e^{x+y}\) for \(0\leq x,y\leq\ln2.\)