reliable paper writing on Continuous Random Variables

Answer the following questions. Your solutions should show all your work. If you use a calculator, indicate what
equations you used to obtain your answer. This homework assignment is due by 5 PM Tuesday, Feb. 24, 2015, for
full credit. There is NO late HW 4, as HW 4 solutions will be posted online after the due date, for pre-exam 1
study.
1. Uniform Random Variable: Model the actual resistive value R0 of a resistor marked as 100
with a 5%
tolerance as a uniform random variable R0 over the range [95, 105]
.
(a) Write the PDF of R0, fR0(R0). Also sketch the PDF.
(b) What is the expected value of R0, E[R0]?
(c) What is the variance of R0, Var[R0]?
(d) What is the probability that the resistor value R0 falls within 1% of 100
, that is, between 99 to 101

? In other words, what is P(99 < R0  101)?
2. Gaussian Random Variable: Model the lifetime of a laptop battery (maximum time it will run on battery
power alone before needing recharging) as a Gaussian random variable X, with mean μx = 10 hours, and
standard deviation x = 2 hours. Use the tables for the CDF and Q-function of a standard normal random
variable (posted on BbLearn in the Handouts folder) as needed.
(a) What is the probability that your laptop battery lifetime is less than or equal to 6 hours, P(X  6)?
(b) What is the probability that your laptop battery lifetime is between 8 and 12 hours, P(8 < X  12)?
(c) What is the probability that your laptop battery lifetime is greater than 18 hours, P(X > 18)? Give
an actual number; don’t just approximate the number as 0.
3. Exponential Random Variable, Joint PDF and Conditional PDF: You call two of your company’s
main clients regularly. The time in minutes of each call to client 1 is modeled as an exponential random
variable T1 with  = 1 phone call/20 minutes. The time in minutes of each call to client 2 is also modeled as
an exponential random variable T2 with the same  = 1 phone call/20 minutes. T1 and T2 are i.i.d. random
variables; they are independent and identically distributed.
(a) Write an expression for the PDF of T1, fT1(t1).
(b) What is the probability that a phone call to client 1 lasts longer than 20 minutes?
(c) Write an expression for the joint PDF fT1,T2(t1, t2).
(d) Find the conditional PDF of T1 conditioned on T2, fT1|T2(t1|t2).
From your conditional PDF, what is the probability that a phone call to client 1 lasts longer than 20
minutes, given that a phone call to client 2 lasted longer than 20 minutes?

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