The temperature X at which a thermostatically controlled switch turns on has probability density function f(x) = {1/2, 59≤x≤600, elsewhere Find E(X) and V(X)
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- A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?Let the random variable X be the time in seconds between incoming telephone calls at a busy switchboard. Suppose that a reasonable probability model for X is given by the pdf: fx(x) = { ie for 0If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.Suppose Uniform(01,02) where the parameters 01 and 02 take the values -4 and -3 respectively. Compute the probability P(Y < y) when y=-3.90.9) 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) for2Let X be a random variable with pdf f(x) = kx*,-1Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).The random variable x follows a uniform probability distribution in the interval (0,1); the probability of obtaining x values outside this range is zero. What is the probability distribution of y = ln x?Suppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of X29)The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.f(x)=k(1-(x-3)²) , 2≤x≤40 otherwise (c) What is the probability that the actual tracking weight is greater than the prescribed weight?P= 0.5 (d) What is the probability that the actual weight is within 0.1 g of the prescribed weight? (Round your answer to four decimal places.)P= 0.1495 (e) What is the probability that the actual weight differs from the prescribed weight by more than 0.45 g? (Round your answer to four decimal places.)P=0.3706Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,