F(x) = 1 2 0 + 1 3 (x-4) 5x - 44 (5 (a) Compute P(X < 0). 0.5 x < -2 -2≤ x < 2 2 ≤ x (b) Compute P(-1 < X < 1). (Round your answer to four decimal places.) 0.6363 X (c) Compute P(0.4 < X). (Round your answer to four decimal places.) 0.1302

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im not sure what did wrong in B) and C). i need help with D) as well

The error involved in making a certain measurement is a continuous random variable \( X \) with the following cumulative distribution function (cdf):

\[
F(x) = 
\begin{cases} 
0 & x < -2 \\ 
\frac{1}{2} + \frac{3}{44} \left(5x - \frac{x^3}{3} \right) & -2 \leq x < 2 \\ 
1 & 2 \leq x 
\end{cases}
\]

### Tasks

(a) Compute \( P(X < 0) \).
- Answer: 0.5 ✓

(b) Compute \( P(-1 < X < 1) \). (Round your answer to four decimal places.)
- Answer: 0.6363 ✗

(c) Compute \( P(0.4 < X) \). (Round your answer to four decimal places.)
- Answer: 0.1302 ✗

(d) Evaluate \( f(x) \) by obtaining \( F'(x) \).
- \( f(x) = F'(x) = \)

(e) Compute \( \tilde{\mu} \).
Transcribed Image Text:The error involved in making a certain measurement is a continuous random variable \( X \) with the following cumulative distribution function (cdf): \[ F(x) = \begin{cases} 0 & x < -2 \\ \frac{1}{2} + \frac{3}{44} \left(5x - \frac{x^3}{3} \right) & -2 \leq x < 2 \\ 1 & 2 \leq x \end{cases} \] ### Tasks (a) Compute \( P(X < 0) \). - Answer: 0.5 ✓ (b) Compute \( P(-1 < X < 1) \). (Round your answer to four decimal places.) - Answer: 0.6363 ✗ (c) Compute \( P(0.4 < X) \). (Round your answer to four decimal places.) - Answer: 0.1302 ✗ (d) Evaluate \( f(x) \) by obtaining \( F'(x) \). - \( f(x) = F'(x) = \) (e) Compute \( \tilde{\mu} \).
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