Discrete Mathematics

Continuous Random Variables

Continuous Random Variables - Joint Probability Distribution

         

Let XX and YY have the joint probability density function: f(x,y)=149xyf(x,y)=\frac{1}{49}xy for 0≤x≤20\leq x\leq2 and 0≤y≤7.0\leq y\leq7. Find the expected value of 3X.3X.

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Let XX and YY have the joint probability density function: f(x,y)=k(x+y)f(x,y)=k(x+y) for 0≤x≤100\leq x\leq10 and 0≤y≤1,0\leq y\leq1, where kk is a constant. Find the marginal probability P(1≤X≤2).P(1\leq X\leq2).

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Let XX and YY have the joint probability density function: f(x,y)=kf(x,y)=k for 0≤x≤50\leq x\leq5 and 0≤y≤8,0\leq y\leq8, where kk is a constant. Find the covariance between XX and Y.Y.

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Let XX and YY have the joint probability density function: f(x,y)=kxyf(x,y)=kxy for 0≤x≤40\leq x\leq4 and 0≤y≤3,0\leq y\leq3, where kk is a constant. Find P(X>Y).P(X>Y).

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Which of the following CANNOT be the joint probability density function of two continuous random variables XX and Y?Y?

(A): f(x,y)=1f(x,y)=1 for 0≤x,y≤1.0\leq x,y\leq1.

(B): f(x,y)=x+yf(x,y)=x+y for 0≤x,y≤1.0\leq x,y\leq1.

(C): f(x,y)=xyf(x,y)=xy for 0≤x,y≤1.0\leq x,y\leq1.

(D): f(x,y)=ex+yf(x,y)=e^{x+y} for 0≤x,y≤ln⁡2.0\leq x,y\leq\ln2.

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