Exercise · ZW-UNIFORM-DISTRIBUTION-008 · ★★☆ Intermediate
If \(X\) is uniform on \([2,8]\), find \(F(5)=P(X\le 5)\).
Choose one option.
Show answer
- B. \(\tfrac12\)
Explanation
\(F(5)=(5-2)/(8-2)=3/6=1/2\). Dividing by \(8\) instead of \(b-a\) gives the wrong \(5/8\).
Review the concept: Uniform distribution
A continuous uniform variable takes values in an interval with the same density at every point, so intervals of equal length have equal probability.
\[f(x)=\frac{1}{b-a},\quad a\le x\le b\]
More practice problems: uniform distribution
- ZW-UNIFORM-DISTRIBUTION-001 If X is uniform on [0,4], find P(X<1).
- ZW-UNIFORM-DISTRIBUTION-002 If X is uniform on [2,6], find E[X].
- ZW-UNIFORM-DISTRIBUTION-003 If X is uniform on [1,5], what is its density at x=3?
- ZW-UNIFORM-DISTRIBUTION-004 If X is uniform on [0,10], find P(3<X<7).
- ZW-UNIFORM-DISTRIBUTION-005 If X is uniform on [-1,3], find P(X>0).
- ZW-UNIFORM-DISTRIBUTION-006 If X is uniform on [0,6], find Var(X).
- ZW-UNIFORM-DISTRIBUTION-007 A uniform variable on [a,b] has mean 5 and variance 3. What is the interval?
- ZW-UNIFORM-DISTRIBUTION-009 If X is uniform on [0,1], find P(X<0.3| X<0.6).