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Elec 430 homework set 1. Rice University Department of Electrical and Computer Engineering.
The current in a semiconductor diode is related to the voltage by the relation . If is a random variable with density function for , find ; the density function of .
Show that if then
Show that for any , , we have
Show that if and are independent the which means and are also independent.
Suppose is a discrete random variable taking values with the following probability mass function with parameter
Find the characteristic function of .
Find and
Consider outcomes of a fair dice . Define events and . Are these events disjoint? Are they independent? (Show your work!)
This is problem 3.5 in Proakis and Salehi.
An information source produces 0 and 1 with probabilities 0.3 and 0.7, respectively. The output of the source istransmitted via a channel that has a probability of error (turning a 1 into a 0 or a 0 into a 1) equal to 0.2.
What is the probability that at the output a 1 is observed?
What is the probability that a 1 was the output of the source if at the output of the channel a 1 is observed?
Suppose and are each Gaussian random variables with means and and variances and . Assume that they are also independent. Show that is also Gaussian. Find the mean and variance of .
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