Exercise · ZW-CUMULATIVE-DISTRIBUTION-FUNCTION-003 · ★☆☆ Basic
\(X\) has density \(f(x)=2x\) on \([0,1]\). What is \(F(x)\) for \(0\le x\le 1\)?
Choose one option.
Show answer
- B. \(x^2\)
Explanation
\(F(x)=\int_0^x 2t\,dt=x^2\). Differentiating \(x^2\) returns the density \(2x\).
Review the concept: Cumulative distribution function
The cumulative distribution function \(F_X\) of a random variable \(X\) gives, for each real number \(x\), the probability \(P\) that \(X\) takes a value less than or equal to \(x\).
\[F_X(x)=P(X\le x)\]
More practice problems: cumulative distribution function
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- ZW-CUMULATIVE-DISTRIBUTION-FUNCTION-007 If F(x)=x^3 for 0≤ x≤ 1, what is the density at x=tfrac12?
- ZW-CUMULATIVE-DISTRIBUTION-FUNCTION-008 For a discrete variable, F(0)=0.2, F(1)=0.5 and F(2)=1, and it only takes the values 0, 1 and 2. Wh…
- ZW-CUMULATIVE-DISTRIBUTION-FUNCTION-009 Let F(x)=(x^2+x)/(6) for 0≤ x≤ 2 (0 before and 1 after). What is P(X>1)?
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