Concept explainers
Repeat Example 2 if the probability density function is
Life Expectancy The life expectancy (in hours) for a particular brand of lightbulb is a continuous random variable with probability density function
(A) What is the average life expectancy of one of these lighlbulbs?
(B) What is the probability that a bulb will last longer than this average?
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- 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) for2arrow_forward4. "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.arrow_forwardIf probability density function of a random varíable X is f(x) = x² for –1SXS1, and %3D O for any other value of x %3D is then, the percentage probabilityParrow_forward6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-oo, 00) is a function f such that f (x) >0 and | f (x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). x-1 00 (b) We can also use probability density functions to find the expected value of the outcomes of the event if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. xf(x) dr yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.arrow_forwardpart D E needarrow_forward3. Which exponential probability density has mean u = ?arrow_forwardSuppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of Xarrow_forwardThe probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by fx(x) = S if æ > 5 if æ < 5 (a) what is the value of C? (b) What is the cumulative distribution function of X?arrow_forwardPlease provide Handwritten answer Question: Find probability distribution function for when: 0 < X < 3 3 < X < 6 X < 0 or X> 0, f(x) = 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill