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 > 0.7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.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.The lifetime of a machine part has a continuous distribution on the interval (0,45) months with probability density function f, where f(x) is proportional to (4+x)-2. Find the probability that the lifetime of the machine part is less than 7 months.Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?hp.com/h20195/v2/GetDocu- Q4. The probability density function of the RV X is f(x) = 5e-kx for x 20. Find 2) bslubsribe ni Ilia ( a) the value of k. b) the probability that x>1. 1.19 ani PHICS c) If Y~N(2,2). X and Y are independent, then find the P(0.25 ≤X ≤ 0.5 and 0.1 ≤Y ≤ 0). sri 200 sulev 19 vode antiw baworla) 126 9di vino b 200 rasl Bus 5 minim ert zienW SHX 1211 65 290100 to af Ye 910255m of b990 neupent1) 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(YLet X and Y has joint probability density function * y? A(X, Y) 81 ,0Let 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