# Past Exam for STAT 400 - APPLIED PROB & STAT I with Millson at Maryland (UMD)

## Exam Information

 Material Type: Exam 2 Professor: Millson Class: STAT 400 - APPLIED PROB & STAT I Subject: Statistics and Probability University: University of Maryland Term: Fall 1997 Keywords: Independent Random VariablesApproximationRandom VariablesThe IndependentIndependentProbability MassSample SpaceContinued...Law of Large NumbersDistribution  ## Sample Document Text

... STAT 400 Hillson TEST #2 Nov. 20, 197 r 1. Suppose X and Yare independent random variables defined on the 2. same sample space each having geometric distribution with parameter p. How is W = X + Y distributed? (Hint: use moment-generating functions) (25 points) Suppose a system consists of 2n components arranged as follows -<: 1,>_<1 1/ 'I 1 ",,_/I:==f) __ 1/ "'1---] Assume that the lifetime of each component is exponentially distributed with a parameter A. Find the probability density function for the system lifetime. (25 points) CONTINUED ON BACK 1 3. Suppose X and Yare random variables defined on the same sample space with the following joint probability table . X""Y 0 1 0 1 1 8 4 1 3 1 8 4 (a) Compute PO' ~ X). (b) Compute the probability mass function of the random variable A = X + Y. (c) Compute the marginal probability mass functions PX(x) andi Py(y). (d) Compute Cov(X,Y). (e) Compute the correlation PX,Y. [25 points] 4...

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