4. Suppose U has a uniform (0, 1) distribution. Then, we could write the p.d.f. as either or fu(t)= 0, for 0 ≤ t ≤ 1; otherwise fu(t) = 1 [0,1] (t). Suppose Y = (b-a)U+ a where a < b. Use the scaling rule to find the p.d.f. of Y, which I suggest you denote by fy so that we do not confuse it with the pdf fu.
4. Suppose U has a uniform (0, 1) distribution. Then, we could write the p.d.f. as either or fu(t)= 0, for 0 ≤ t ≤ 1; otherwise fu(t) = 1 [0,1] (t). Suppose Y = (b-a)U+ a where a < b. Use the scaling rule to find the p.d.f. of Y, which I suggest you denote by fy so that we do not confuse it with the pdf fu.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![4. Suppose \( U \) has a uniform \((0, 1)\) distribution. Then, we could write the p.d.f. as either
\[
f_U(t) =
\begin{cases}
1 & \text{for } 0 \leq t \leq 1; \\
0 & \text{otherwise}
\end{cases}
\]
or
\[
f_U(t) = \mathbf{1}_{[0,1]}(t).
\]
Suppose \( Y = (b-a)U + a \) where \( a < b \). Use the scaling rule to find the p.d.f. of \( Y \), which I suggest you denote by \( f_Y \) so that we do not confuse it with the pdf \( f_U \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2F0a0f4cec-a70c-4037-a366-c37ebb8eac32%2Fmejy8q4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Suppose \( U \) has a uniform \((0, 1)\) distribution. Then, we could write the p.d.f. as either
\[
f_U(t) =
\begin{cases}
1 & \text{for } 0 \leq t \leq 1; \\
0 & \text{otherwise}
\end{cases}
\]
or
\[
f_U(t) = \mathbf{1}_{[0,1]}(t).
\]
Suppose \( Y = (b-a)U + a \) where \( a < b \). Use the scaling rule to find the p.d.f. of \( Y \), which I suggest you denote by \( f_Y \) so that we do not confuse it with the pdf \( f_U \).
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