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G canvas.fsu.edu + FSU session expired Exponenial and Poisson Distributions and the Poisson Process quiz alinia Sling TV - Home Return Submit 1 10 points Let X ~ Pois(1). Mark all of the following which are true. VX = 12 EX =1 O The support of X is the set X = {0, 1, 2, .. .}. The probability mass function f (a) for X is given by f (a) = de-xx. 2 10 points Let X ~ Exp()). Mark all of the following which are true. O The probability density function f (x) for X is given by f (x) = Ne Ax The support of X is the set X =] [0, co). O VX = 1/12 EX =1 3 10 points Suppose that the times between events occurring are independent exponential random variables X with rate parameter ) = 15 and are measured in minutes. What would be the rate parameter if the random variable were instead measured in seconds? Hint: Define a new random variable Y (measured in seconds) to be an appropriate transformation of X (measured in minutes). I.e., this is a unit conversation problem. Let Ax = 15 and the value of Ay which will be the rate parameter for Y. Type your answer... OCT 11 astv I ?Type your answer". ' )l P f i 10 points [3 ' Suppose that the times between events occurring are independent Exponential random variables with rate parameter A = .1.The number of events occurring in the time interval [10, 20] will follow a Poisson distribution with what parameter? El ' V 7 \"ml : Type your answer.\" i i u 1 .y , ; > ; 4 2 10 points _ Let N(t) be a Poisson process with rate parameter A > 0. Mark all of which are true' r ' 3 N03) is the number of events'which have occurred up to time t. 4 N(5) N Pois(5 A). k 5 The times between events occurringfollow the Exponential(A) distribution. The amount of time between events occurring are independent Exponential random variables. IE N(t) = A t. y N(t) : At. If T is the amount of time between the current event and the last event occurring, E T : 1/ A