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}.

Part (a): Sketch X as a function of ζ.The random variable X is defined as X = e^ζ, where ζ is…

Answered: Problem 3. (16 points) Let ¢ be a point…

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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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?
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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}.