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- Question 1 function given by Suppose that X and Y have a joint probability density ce-3r-5y if x, y 20 fx.x(x, y) = %3D otherwise Dete the value of the normalization constant c. (b Find the marginal probability density function fx and state the name of the distribution of X. (YFind the conditional probability density function fyjx=z- (Y Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely fxx(x, y) = J12ye-3z-2y if r, y 20 otherwise OWhat is the probability P(Y2 > 2X > 0) ?The variance is a measure of the dispersion of the random variable about the mean. Variance example 1. Consider the density function (p +1)æP 0 < x < 1 f(x) otherwise where p is greater than -1. compute the Var(X)Book name Mathematical statistics by John Fred 8th edition Chp 3 Question 78
- Section: Probabilty Density Functions1. Develop a random variate (composition method) generator for the random variable X with the probability density function where I represents the indicator function. 5 f(x)=e*I(x 0) 4 a. Implement this generator to generate 500 random variates. b. Compute the sample mean and sample variance of these 500 variates and compare with the theoretical values. c. Plot the histogram of these 500 variates and compare the histogram with the graph of f(x).Question Six: Consider a continuous random variable X representing the time taken to assemble a part. The variable X is known to be between 0 and 2 minutes, and its probability density function (pdf),f(x), is given by f(x) =, 0< x< 2 (a) Show it is a valid density function (b) Graph this density function. (c) Find the probability that X is between 1 and 2. (d) Find the mean (or expected value E(X) and the variance for this probability distribution.
- 2.70 Let X and Y be random variables with joint density function (4xy, 0< x,y< 1, f(x,y)= {0, elsewhere. Find the expected value of Z = √X² + y².Section: Probabilty Density Functions1. The density function for random variable X is f(x). Find variance for the random variable X. Leave your answers as reduced fractions. f(x) = {16 x+0A random variable X has the density function: Ix(x) = {6 (2 - x) 1QUESTION 3 Suppose that the continuous random variables X and Y have the joint density function 4xy x, y = [0, 1] 0 otherwise f(x, y) = and suppose the expected values of Y is E(Y) Round to 4 decimal places if needed. = 3. Find the variance of Y.Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.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