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2003 University of Illinois at Chicago ECE 341 V. Goncharoff
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ECE 341 - Probability and Random Processes for Engineers
Homework #7 (write answers here, show work on paper stapled to this cover sheet)
Problem 1.
Continuous random variable X is uniformly distributed between −5 and +10.
a) What is μ (^) X?
b) What is [ ]
2 E X?
c) What is σ (^) X?
d) What is P [ 0 ≤ X ≤ 2 ]?
Problem 2.
Continuous random variable X is Gaussian with zero mean value and σ (^) X = 2.
a) What is [ ]
2 E X?
b) What is P [ X > 2 ]?
c) What is P [ 0 ≤ X ≤ 2 ]?
2003 University of Illinois at Chicago ECE 341 V. Goncharoff
Problem 3.
Zero-mean Gaussian random variable N is known to be in the range −1 to +
volts with 60% probability.
a) What is Var[ N ]?
b) What is the probability that N > 2?
Problem 4.
The random variable X has probability density function
0 , otherwise.
x x f (^) X x
a) Write an algebraic expression for the CDF F (^) X ( x ):
b) What is [ 4 ] 3 4
1 P < X ≤?
c) What is [ ] 2
1 8
P^1 < X ≤?
