A3P3

Let the random variable \(X\) had the probability density function given by: \(f(x) = c(x+{{ params.offset }}), {{ params.lb }} \lt x \lt {{ params.ub }}\)

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?

\( F(x) = \begin{cases} 0, x \leq {{ params.lb }} \\\\ ?, {{ params.lb }} \lt x \lt {{ params.ub }} \\\\ 1, x\geq {{ params.ub }} \end{cases} \)

Answer Section

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Part 3

What is \(P({{ params.part3.lb }} \leq X \leq {{ params.part3.ub }})\)

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.