A random variable x has a density function f(x) = c(x+1) where 0 < x < 2| 2
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A: The pdf of X is fx=3x2,0≤x≤1 EX=∫01x*fxdx=∫01x*3x2dx=3∫01x3dx=3 x4401=3144-0=34=0.75
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Q: Then E (X) is equal to
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Q: Let X be a random variable of a continuous type and let it be given by Mx(t) = 1 t<1 (1-t)² Find the…
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- The probability density function of a continuous random variable X is given by y=4−2x from x=1 to x=2 . (a) Draw the graph of the density curve for the continuous random variable. (b) Verify it is a probability density function. (c) Compute P(X≥1.5) .Let x be a continuous random variable with density function +K 9. 0The random variable X has the density function: f(x) = (8- x), Osxs2 (a) The standard deviation of X is (Round to four decimal places including any zeros.) (b) According to the Chebyshev's theorem, for k= 1.71, the probability P(O8)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the joint probability density function of the order statistics X(2), X(4), X(6) for n = 7.Determine the mean value of the continuous exponentially distributed random variable 1 (x-a) e b x>a with density function, fy(x)={b XThe life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by 2e-(x+2y) X> 0, γ> 0 fx,ylx,v) = { else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.7772 b. 0.3935 10 c. 0.606 d. 0.6318 e. 0.3669Let X be the proportion of new restaurants in a given year that make a profit during their first year of operation, and suppose that the density function for X is ƒ(x) = 20x³(1 − x) Find the expected value and variance for this random variable. E(X) = = Var(X) 0 ≤ x ≤ 1Let X be a continuous random variable with density function be-bx for a > 0 f (x) = otherwise where b > 0. - find M(t) the moment generating function of X, then what is E(x) ?Let X and Y continuous random variable with joint density function f(x, y) = (²³/1 (2 - x - y) x - y) for 0 < x, y < 2; 0 < x + y<2 otherwise. 0 What is the conditional probability P(X < 1| Y < 1)?Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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