The pdf of a continuous random variable X is given by: [x(x) = { *xx +2x² 0≤x≤6 0 elsewhere Determine the value of E[X].
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![The pdf of a continuous random variable X is given by:
[x(x) = { *xx
0≤x≤6
0
elsewhere
Determine the value of E[X].
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- Get the variance and standard deviationA 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?Suppose 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 denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)x where -1 < 0. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) - 1 1 0 (x - 1) - - 2 0 (1-7) - -n ΣIn(X) Eln(X;) n 2 0 (1 + 7) 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣΙn(Χ;) -n - 1 1 n ΣIn(Χ.) Compute the estimate for the given data. (Round your answer to two decimal places.)Consider the function: f(x)= −1 − x^2 Which of the following is true? A. This function is a pdf only for some values of random variable B. This function cannot be a pdf for any set of values of random variable C. None of these D. This function is a pdf for any set of values of random variable.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 0Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)Let X be a random variable with pdf f(x) = kx*,-1Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1The standard deviation of X, denoted SD(X), is given by SD(X) = /Var(X). Find SD(aX + b) if X has varianc of o2.Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of Xis F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, X-0.95, x=0.73, x=0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+)-1 -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Lin(X)) n Zn(x)) -n -n Din(x) n in(X) ΣΟΧ) 1SEE MORE QUESTIONSRecommended textbooks for youGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill