Answered: Problem 2) If X is an Erlang (n, à)… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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11:43
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Exercise#8
EENG 3421-Advanced Engineering Analysis
Exercise #8
Problem 1) If Y is an exponential random variable with Var[Y] =25, find the following:
a) What is the PDF of Y?
b) What is E[Y]?
c) What is P[Y>5]?
Problem 2) If X is an Erlang (n, λ) random variable with parameter 1/3 and expected value
E[X]-15, find the following:
a) What is the value of the parameter n?
b) What is the PDF of X?
c) What is Var[X]?
Problem 3) If Y is an Erlang (n=2, λ-2) random variable, find the following:
a) What is E[Y]?
b) What is Var[Y]?
c) Find P[0.5Y<1.5].
c) What is E[X]?
d) What is E[X³]?
e) What is Ele?
Problem 4) If X is a continuous uniform (-5, 5) random variable, find the following:
a) What is the PDF of X?
b) What is the CDF of X?
Problem 5) If X is a continuous uniform random variable with expected value E[X] = 7 and
variance Var[X]-3, then what is the PDF of X?
Problem 6) Radars detect flying objects by measuring the power reflected from them. The
reflected power of an aircraft can be modeled as a random variable Y with PDF:
5,6)=²*
0
y20
otherwise
where PO> 0 is some constant. The aircraft is correctly identified by the radar if the reflected power
of the aircraft is larger than its average value. What is the probability P[C] that an aircraft is
correctly identified?
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