Suppose that f(x) = 1.5x² for -1 < x < 1. Determine the following probabilities: a) P(0 < X) = 0.5 b) P(0.2 < X) = 0.496 (Round the answer to 3 decimal places.) c) P(-0.5 ≤ x ≤ 0.5) = 0.125 (Round the answer to 3 decimal places.)
Suppose that f(x) = 1.5x² for -1 < x < 1. Determine the following probabilities: a) P(0 < X) = 0.5 b) P(0.2 < X) = 0.496 (Round the answer to 3 decimal places.) c) P(-0.5 ≤ x ≤ 0.5) = 0.125 (Round the answer to 3 decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![**Probability Calculations for a Given Function**
Suppose that \( f(x) = 1.5x^2 \) for \( -1 < x < 1 \). Determine the following probabilities:
a) \( P(0 < X) = \boxed{0.5} \)
b) \( P(0.2 < X) = \boxed{0.496} \) (Round the answer to 3 decimal places.)
c) \( P(-0.5 \leq X \leq 0.5) = \boxed{0.125} \) (Round the answer to 3 decimal places.)
d) \( P(X < -2) = \boxed{1} \)
e) \( P(X < 0 \text{ or } X > -0.5) = \boxed{-1} \)
f) Determine \( x \) such that \( P(x < X) = 0.05 \). (Round the answer to 3 decimal places.)
\[ \boxed{-0.965} \]
Note: This problem involves calculating probabilities for a given probability density function \( f(x) \). The answers provided include a mix of numerical values and constraints applied to \( x \) values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bad4e48-dad8-4710-a64b-b24b80d1efcf%2F5bdbc18e-04db-4e7c-b360-1d549e53157f%2Fvbaq28w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability Calculations for a Given Function**
Suppose that \( f(x) = 1.5x^2 \) for \( -1 < x < 1 \). Determine the following probabilities:
a) \( P(0 < X) = \boxed{0.5} \)
b) \( P(0.2 < X) = \boxed{0.496} \) (Round the answer to 3 decimal places.)
c) \( P(-0.5 \leq X \leq 0.5) = \boxed{0.125} \) (Round the answer to 3 decimal places.)
d) \( P(X < -2) = \boxed{1} \)
e) \( P(X < 0 \text{ or } X > -0.5) = \boxed{-1} \)
f) Determine \( x \) such that \( P(x < X) = 0.05 \). (Round the answer to 3 decimal places.)
\[ \boxed{-0.965} \]
Note: This problem involves calculating probabilities for a given probability density function \( f(x) \). The answers provided include a mix of numerical values and constraints applied to \( x \) values.
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