Problem 3. (16 points) Let ¢ be a point selected at random uniformly from the unit interval [0,1]. Consider the random variable X = es. (a) (b) ts) Sketch X as a function of C. Find and plot the CDF of X. (c) Find the probability of the events {X > √e} and {e0.25 < X ≤ e0.75}.
Problem 3. (16 points) Let ¢ be a point selected at random uniformly from the unit interval [0,1]. Consider the random variable X = es. (a) (b) ts) Sketch X as a function of C. Find and plot the CDF of X. (c) Find the probability of the events {X > √e} and {e0.25 < X ≤ e0.75}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 2E
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![Problem 3. (16 points) Let ¢ be a point selected at random uniformly from the unit interval [0,1].
Consider the random variable X = es.
(a)
(b)
ts) Sketch X as a function of C.
Find and plot the CDF of X.
(c)
Find the probability of the events {X > √e} and {e0.25 < X ≤ e0.75}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd050aa83-a110-46ef-80f2-445fe1eebe4e%2F5d26c3d4-a305-462e-b4ee-0454751522dd%2F31isi9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3. (16 points) Let ¢ be a point selected at random uniformly from the unit interval [0,1].
Consider the random variable X = es.
(a)
(b)
ts) Sketch X as a function of C.
Find and plot the CDF of X.
(c)
Find the probability of the events {X > √e} and {e0.25 < X ≤ e0.75}.
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