نقطتان )2( Q4) Consider the following joint probability density function with random variable (X and Y, what is P(X>2|Y>2 X=1 X=2 X=3 X=4 X=5 Y=1 0.01 0.05 0.06 0.01 0.01 Y=2 0.02 0.03 0.04 0.05 0.06 Y=4 0.07 0.08 0.09 0.01 0.09 Y=8 0.09 0.01 0.01 0.01 0.01 Y=10 0.09 0.07 0.01 0.01 0.01 0.485 0.335 0.379 O 0.409 O 0.439 O
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- a. Explain the difference between the method of moment generating function and the method of incarnation to find the probability density function of a random variable b. Let X1, X2, X3 ,,,,, each of them has Poisson distribution with parameter lamda 1, lamda2, lamda3,........ i. Get the probability distribution of Y=X1+X2+....Xn ii. Get the mean and variance of Y c. Y1 and Y2 be a joint probability function as shown below in the screenshot imageU=Y1/(Y1+Y2), Using the method of incarnation (Jacobian), find the probability density function of UThe number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.the popularity density function f(x) for a uniform random variable X defined over the interval [2,10] is?
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