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# 5 pair of RVs - PowerPoint PPT Presentation

5 pair of RVs. 5-1: joint pmf. In a box are three dice. Die 1 is normal; die 2 has no 6 face, but instead two 5 faces; die 3 has no 5 face, but instead two 6 faces. The experiment consists of selecting a die at random, followed by a toss with that die.

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## PowerPoint Slideshow about ' 5 pair of RVs' - conor

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### 5 pair of RVs

• In a box are three dice. Die 1 is normal; die 2 has no 6 face, but instead two 5 faces; die 3 has no 5 face, but instead two 6 faces.

• The experiment consists of selecting a die at random, followed by a toss with that die.

• Let X be the die number that is selected, and let Y be the face value of that die.

• Find P(X = x, Y = y) for all possible x and y.

• A packet switch has two input ports and two output ports. At a given time slot, a packet arrives at each input port with probability and is equally likely to be destined to output port 1 or 2. Let X and Y be the number of packets destined for output ports 1 and 2, respectively. Find the pmf of X and Y.

• Three outcomes for an input port can take the following values: (i) “n”, no packet arrival; (ii) “a1”, packet arrival destined for output port 1; (iii) “a2”, packet arrival destined for output port 2.

• We pick a message, whose length N follows a geometric distribution with parameter 1-p and SN={0,1,2,…}.

• Find the joint pmf and the marginal pmf’s of Q and R, where Q is the quotient in the division of N by constant M, and R is the number of remaining bytes.

• Joint pdf is given by:

• Find c.

• Find marginal pdf’s

• Find P[X+Y1]

• The total number of defects X on a chip is a Poisson random variable with mean .

• Each defect has a probability p of falling in a specific region R and the location of each defect is independent of the locations of other defects.

• Find the pmf of the number of defects Y that fall in the region R.

• X is selected at random from the unit interval; Y is then selected at random from the interval (0, X).

• Find the cdf of Y.

• A system with standby redundancy has a single key component in operation and a duplicate of that component in standby mode.

• When the first component fails, the second component is put into operation.

• Find the pdf of the lifetime of the standby system if the components have independent exponentially distributed lifetimes with the same mean .