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Omni-MATH / Natalie has a copy of the unit interval [0,1] that is colored white. She also has a black marker, and she colors the interval in the following manner: at each step, she selects a v…

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problem

Natalie has a copy of the unit interval [0,1][0,1] that is colored white. She also has a black marker, and she colors the interval in the following manner: at each step, she selects a value x∈[0,1]x \in[0,1] uniformly at random, and (a) If x≤12x \leq \frac{1}{2} she colors the interval [x,x+12][x, x+\frac{1}{2}] with her marker. (b) If x>12x>\frac{1}{2} she colors the intervals [x,1][x, 1] and [0,x−12][0, x-\frac{1}{2}] with her marker. What is the expected value of the number of steps Natalie will need to color the entire interval black?
Plain-text mathematical notation (without MathML)
Natalie has a copy of the unit interval [0,1] that is colored white. She also has a black marker, and she colors the interval in the following manner: at each step, she selects a value x∈[0,1] uniformly at random, and (a) If x≤(1)/(2) she colors the interval [x,x+(1)/(2)] with her marker. (b) If x>(1)/(2) she colors the intervals [x,1] and [0,x−(1)/(2)] with her marker. What is the expected value of the number of steps Natalie will need to color the entire interval black?
Original LaTeX notation
Natalie has a copy of the unit interval $[0,1]$ that is colored white. She also has a black marker, and she colors the interval in the following manner: at each step, she selects a value $x \in[0,1]$ uniformly at random, and (a) If $x \leq \frac{1}{2}$ she colors the interval $[x, x+\frac{1}{2}]$ with her marker. (b) If $x>\frac{1}{2}$ she colors the intervals $[x, 1]$ and $[0, x-\frac{1}{2}]$ with her marker. What is the expected value of the number of steps Natalie will need to color the entire interval black?

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task_id
fd087473-d02f-5908-b5aa-03e34f382d37
task_key
test--fd087473-d02f-5908-b5aa-03e34f382d37
task_revision_id
1
config / split
/ test

Official source

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