Consider the following function f(y) = }4374 ¡y® for -c

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Consider the following function

\[ f(y) = 
  \begin{cases} 
   \frac{1}{4374} y^8 & \text{for } -c < y < c \\
   0 & \text{elsewhere} 
  \end{cases}
\]

1. Find the constant \( c \) such that \( f(y) \) is a density function of \( Y \).

2. Find the cumulative distribution function of \( Y \), \( F(y) \).

3. Find the probability that \( Y \) is at least -1.4 and at most 2.6.

4. Find the probability that \( Y \) is at most 2.5 given it is at least -1.3.
Transcribed Image Text:Consider the following function \[ f(y) = \begin{cases} \frac{1}{4374} y^8 & \text{for } -c < y < c \\ 0 & \text{elsewhere} \end{cases} \] 1. Find the constant \( c \) such that \( f(y) \) is a density function of \( Y \). 2. Find the cumulative distribution function of \( Y \), \( F(y) \). 3. Find the probability that \( Y \) is at least -1.4 and at most 2.6. 4. Find the probability that \( Y \) is at most 2.5 given it is at least -1.3.
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