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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Problem: The probability density function of a random variable is given by the exponential
distribution
Find the probability that
f(x) = {0.55e−0.55x 0 < x, O elsewhere}
a. the time to observe a particle is more than 200 microseconds.
b. the time to observe a particle is less than 10 microseconds.

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Just d,e
answer only part b .
4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point is called time headway. Now, let X = the time headway for two randomly chosen consecutive cars on a highway during a period of heavy traffic flow. The following probability density function of X is suggested by traffic experts: f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec) 0 otherwise a. Draw f(x) from x = 0 to x= 10 sec. b. Find P(X ≤ 5 sec) and show it on the figure you have drawn. c. What is E[X] and Var[X] ? d. Find Cumulative Distribution Function of X.
Use the following to answer the next 3 questions. The random variable X is described by the following pdf: f(x) = {3x 3x-4, x > 1 otherwise 19. What the cumulative density function? a. F(x) = 1 b. F(x) = -3 -x-³ c. F(x): = 1-x-3 d. F(x) = 3x¯4 20. What is the probability X will be less than 1.2? a. 0.634 b. 0.421 c. 0.579 d. 0.113 21. What value represents the 95th percentile? a. 2.71 b. 1.65 c. 1.96 d. 1.17
I don't understand this.
Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.
9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): 3 f (x) ={32 (x- 2)(6-x) for2
If a random variable X ∼ Exponential(1). Find the distribution of Y = X/λ.
Please do part b
ONLY NEED PART E
1. The probability density function of a random variable X is given by f (x) : 1 ex/300 300 for x 2 0 and f (x) = 0 for x < 0. Find P (X s 600).

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