Suppose a continuous random variable X~Fx(x): f(x,y) = { 1/4e^-1x/4, if x≥0 0, x<0 } What is the cumulative density function of Y=min{2,X}?
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Suppose a continuous random variable X~Fx(x):
f(x,y) = {
1/4e^-1x/4, if x≥0
0, x<0
}
What is the cumulative density
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- The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Q2) The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function as shown below, Find the probability that a bottle of this medicine will have a shelf life of anywhere between 40 and 120 days 20000 0Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.The median of the random variable X whose probability density function 3 =x² ,0 < x < 2 - - f(y) = }2 ,0. W. isSuppose that two random variables X and Y have the joint PDFfXY(u, v) = {60(u^2)v u ≥ 0, v ≥ 0, and u + v ≤ 1, 0 otherwise.(a) Are X and Y independent?(b) What is the marginal distribution fX(t)?(c) What is Pr[X ≥ Y]? (To set up the right integral, it might help you to draw the rangeof (X, Y) in the uv-plane and identify the region within that range where u ≥ v.)2) Let X be a continuous random variable with PDF 0Suppose that X follows the Weibull distribution with pdf f(r) = Br1e on r> 0, %3D where B> 0. (a) By integrating using the substitution u = , and checking what happens to the integration limits, show that E(X)-r (등+1). %3D (b) Calculate the numerical value of the variance of the Weibull distribution when B= }.Differentiate. f(w) = w / [w + (d/w)]A random variable is called a power law random variable ifP(X > t) = max{1/(t^α), 1}for some α. What is the density of X? Compute the mean of X when α > 1. What happens if α < 1?Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON