3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an observed value of a random variable X 4 U (0, 6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P(Y > y) for any given y. (c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of Y?
3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an observed value of a random variable X 4 U (0, 6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P(Y > y) for any given y. (c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of Y?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 22E
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![3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an
observed value of a random variable X 4 U (0, 6). The random variable X divides the
interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively.
Denote by Y the length of the shorter of the two intervals.
(a) Draw a picture which illustrates the value of Y as a function of the possible values
of X.
(b) Describe the support of Y and find the probability P(Y > y) for any given y.
(c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of
Y?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1426004-0ad6-48d6-9ffb-3c170d243421%2F773af251-3f51-40ab-9200-3659f1eeb253%2Fizbfbqj_processed.png&w=3840&q=75)
Transcribed Image Text:3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an
observed value of a random variable X 4 U (0, 6). The random variable X divides the
interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively.
Denote by Y the length of the shorter of the two intervals.
(a) Draw a picture which illustrates the value of Y as a function of the possible values
of X.
(b) Describe the support of Y and find the probability P(Y > y) for any given y.
(c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of
Y?
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