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- 12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))4. The monthly revenue (in millions) of a local gaming company is represented by a continuous random variable X having the probability density f(x) = (1 - (x-1)²), 0 < x < 2, 0, elsewhere Find the mean and variance of X.Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
- Q3/ If the M.g.f. of random variable x is : M(t) = (0.75 + 0.25 e')" x = 0,1, 2,3, .,n 1- if (n = 4) find the Median and Pr(0 sx< 1)? 2-if (n = 5) find var(x), E X(X – 1) ? 3- find c .d. f. of X?الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)Let X1, X2,...,X, be a random sample from a distribution with density function e if x > 0 f(x; 0) elsewhere What is the maximum likelihood estimator of 0 ?b) The probability density function of random variable X is given as: - Вх {*5 if 0 < x < 1 otherwise f(x) = If the expected value of the random variable X is 1/3. Find the values A and B.Let Zw distributed as Chi square random variable with n degree of freedom. Find the limiting distribution of Wn = Zw/n29. The random variable X has probability density function, f(x) where k 1Recommended 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