der the random variable X with density function f (x) = x² for –1< x <1 (an | other values of X). Determine the values of Y for which the transformed random variab X² is non zero. 1
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- 7let x continuous random Variable ea Probabil;ty density function fx (X), The firobability distribution of a random Variable Y= ax+b (azo, b fixed)is: it has is 2. 3-A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is given by: ays if y > yo fG) = ya+1 (0, elsewhere i) Derive the mean of Y. Show all necessary steps. (7) Show whether or not that the variance of Y is ays (а-2)(а-1)2" ii) (8)Q 4.2. Let (X, Y) be a random variable with the following density: {152-2 0 £x,x (x, y) = { 1. Express E(Y|X) in terms of X. 2. Express Var(XY) in terms of Y. 0 < x < y < 1, otherwise.
- The random variables X and Y have a joint probability density function given by f(x, y) = way, 0 < x < 3 and 1 < y < x, and 0 otherwise.The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 825. Let X and Y be continuous random variables with joint density function for 0Let x be a random variable with a density function I (2) = { "0, 6x (1 – a), 0 < x < 1 elsewhere By finding the fırst and second moments, calculate the variance of x [1] (answer correct to 1 dp)The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 < x<1 f(x) = - 0, 5 elswhere Find the stàndard deviation of above stated continuous random variable (X)Recommended 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