4.14 Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function | 2(=+2), 0
Q: Determine the variance of Z.
A: Helpful formulas (i)VaX=a2VX(ii)VC=0,where c is the constant(iii)VaX+ bY=a2VX+ b2VY
Q: how to calculate the variance?
A: Given The data is as follows: Overall mean = 4.07 Variance = 0.00130 SD = 0.1140
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A: mean=μ=E(X)
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Q: Younger Adults (average age 31) Older Adults (average age 72) 94738 79678 62845 67668 75266 97869
A: For younger adults: x x-x (x-x)2 9 3.53 12.4609 4 -1.47 2.1609 7 1.53 2.3409 3 -2.47…
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Q: * 2.4.5.6-8-17 11 17 20 24 32 Xị 3 5 9 3 fi 1. 4) 5n 00
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- Q2) The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the below density function , Find the probability that a bottle of this medicine will have a shelf life of anywhere between 60 and 120 days 20000 02.5.12.) The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density func- tion given by f(x) = { ae-(1/5)x 0, x>0 elsewhere. Find (a) The value of a that makes f(x)a probability density function. (b) The probability that this individual will talk (1) between 8 and 12 minutes, (2) less than 8 minutes, (3) more than 12 minutes. (c) Find the cumulative distribution function, F(x).11. The weekly demand for propane gas (1000s of gallons) at a certain facility is a continuous variable with density function shown in attached image Determine both the mean value and the median. In the long run, in what proportion of weeks will the value of x be between the mean value and the median?Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by ky² ( 1 - y)3 0I was calculating a conditional density function and I got an answer of 2x+3y all over 2x+3/2. When I checked the answer, it was 4x+6y all over 4x+3. Those two answers are the same, but my question is--is there some protocol as far as what is proper form to express an answer in when dealing with density functions?Ex1: Suppose that f(x)=e* for x>0 Determine the following: a/P(X=1),P(X = 2 or X = 3) b/ P(X > 2), P(1 ≤ x ≤ In 5) c/ Mean and variance of X d/ The cumulative function F(x)1.2. Assume that Billy's driving time to class is uniformly distributed from 15-20 minutes in good weather, and uniformly distributed from 25-30 minutes in bad weather. Let the RV X describe Billy's drive time. If the probability of good weather is 2/3. a) .describe mathematically the PDF of X. b) ..describe graphically the PDF of X. c) .find the probability that Billy's drive time is >18 minutes. d) .find the Expected Value of Billy's drive time, irrespective of the weather.7. Suppose a number is drawn at random from a distribution whose pdf is f(x) = 3x² for 0 ≤ x ≤ 1 (this is the pdf that was validated in #4 from above). Find the probability that the number lies in the interval [0,1/3], i.e., evaluate P(0 ≤ x ≤ ¹). 3 (Probability Density Function)Let x denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a student, and suppose that x has density func-tion f(x)=0.5x for 0<x<2 mean: 1.33 meadian: 1.41 What proportion of checkout times are within one-half hour of the mean time? What propor-tion are within one-half hour of the median time? NOTE: answers are 0.615 & 0. 707 but I am not getting it rightSEE MORE QUESTIONSRecommended textbooks for youCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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