A3P3

Contents

A3P3#

Let the random variable $X$ had the probability density function given by: $f (x) = c (x + p a r a m s . o f f s e t), p a r a m s . l b < x < p a r a m s . u b$

Where appropriate round answers to 3 decimal places.

Part 1#

What is the value of $c$ which makes this a valid probability distribution function?

Answer Section#

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Part 2#

What is the missing expression in the CDF below?

$F (x) = {\begin{cases} 0, x \leq p a r a m s . l b \\ ?, p a r a m s . l b < x < p a r a m s . u b \\ 1, x \geq p a r a m s . u b \end{cases}$

Answer Section#

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Part 3#

What is $P (p a r a m s . p a r t 3. l b \leq X \leq p a r a m s . p a r t 3. u b)$

Answer Section#

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Part 4#

What is the 23th percentile of this distribution? Hint: you’ll need the quadratic formula.

Answer Section#

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Part 5#

What is the expected value of $X$ ?

Answer Section#

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Part 6#

What is E[ $X^{2}$ ]?

Answer Section#

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Part 7#

What is the variance of $X$ ?

Answer Section#

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Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.