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Let Y1 and Y2 have the joint probability density function
Chapter 5, Problem 8E(choose chapter or problem)
Let \(Y_{1}\) and \(Y_{2}\) have the joint probability density function given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} k y_{1} y_{2}, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right. \)
a. Find the value of k that makes this a probability density function.
b. Find the joint distribution function for \(Y_{1}\) and \(Y_{2}\).
c. Find \(P\left(Y_{1} \leq 1 / 2, Y_{2} \leq 3 / 4\right)\).
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(1 Reviews)
QUESTION:
Let \(Y_{1}\) and \(Y_{2}\) have the joint probability density function given by
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} k y_{1} y_{2}, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right. \)
a. Find the value of k that makes this a probability density function.
b. Find the joint distribution function for \(Y_{1}\) and \(Y_{2}\).
c. Find \(P\left(Y_{1} \leq 1 / 2, Y_{2} \leq 3 / 4\right)\).
ANSWER:Step 1 of 4
The joint probability density function of \(Y_{1}\) and \(Y_{2}\) is given as
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} k y_{1} y_{2}, & 0 \leq y_{1} \leq 1,0 \leq y_{2} \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right.\)
Using this, we need to find the required values.
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