6.43. Let X and Y be, respectively, the smallest and the largest values of two uniformly distributed values on (0,1). Find the conditional density function of Y given X € (0,1). Also, show that X and Y are not independent. = x,
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- A student has 3 volumes of short stories and 2 novels on a bookshelf. She selects 3 books at random to take home over vacation. A random variable X is defined to be the number of novels selected. Find the values assumed by X and its density function.The time T a business is closed after a fire has the cumulative distribution function (부)- 3 1 1 F7(t) = t>0 t+1 otherwise = VT. The cost to the insurer is X = Determine the density of X for x > 0.endent. 3.60 The joint probability density function of the ran- dom variables X, Y, and Z is ry=", 0 }, 2 < Z < 3); (d) P(0 < Z < 2 | X = , Y = }). 75°F Mostly cloudy
- Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 01) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.The joint density of X and Y is given by, ху, Iw(x, y) = (x² +: 0 l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(YX is a uniform random variable over the interval (3, 5). Find the density function of X for the interval (3, 5)Let X and Y has joint probability density function * y? A(X, Y) 81 ,0Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table. Find: 1) The Covariance Cov(X,Y)? (Cov(X,Y) = MxY-MxMY) 2) The correlation (pxy) between X and Y where Pxy = Cov(X,Y) PXPY Y 3 fx(x) f(x,y) 1 2 1 1/4 1/4 0 X 2 0 1/4 1/4 fy(y) Note that 2 n=2 n=3 Px² = Σn²±²x² f(x, y) - μ and py² = Σ3y² f(x, y) – µ Zk=0The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2, 0 < y1 < 1, 0 < y2 < 1,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Could you tell whether Y1 and Y2 were independent or not without finding marginaldensity functions? Explain.c) Find P(Y1 + Y2 < 0.2).d) Find P(0 < Y2 < 0.5|Y1 = 0.4).Let X be a random variable that represents the number of processes currently running in your computer, between 50 and 200 processes. Let Y be a random variable that represents your computer's internal temperature between 20 and 100 celcius. Compute the correlation between these two random variables if we model this situation with the joint density function, where K is a scaling constant. To show your work set up all your intervals correctly.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON