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Assignment Task:

1. One drives to FIU and on any given day, the probability of getting a speeding ticket is 0.15.   
a. What is the probability that on their 10th trip (day of an exam), the driver will be pulled over for speeding and have their license suspended?  Assume the fourth speeding ticket leads to license suspension. 
b. What is the expected number of the trip before license suspension?   
2.  In a class of 20 students, 5 are undergrads.  For the final project, students randomly divided into 5 groups.  What is the probability that each group has only 1 undergrad? 
3.  How many unique sequences can be formed by rearranging letters C, L, A, S, and S?   
4.  Data packets containing 64 bits are transmitted over a communication channel.  A transmitted bit is received incorrectly with probability p=0.01.  The packet is coded in such a way that a bit error of 2 or less can be corrected.  What is the probability that a packet is decoded correctly? 
5.  A person regularly spends $10 to buy energy drinks.  Typically, one is able to buy exactly 2 energy drinks, but during promotions, one is able to buy exactly 3.  The probability of promotion is 0.6. 
a. What is the expected value of the number of drinks bought? (EEE5543)
b. What is the expected value of the unit cost of the drinks?

6. A bad marksman takes 10 shots at a target with the probability of hitting the target with each shot of 0.1, independent of other shots. Z is the random variable representing the number of hits. 
a) Calculate and plot the PMF of Z. 
b) Calculate and plot CDF of Z. (You may desire to manual adjust the plot for our convention) 
c) What is the probability that 3< Z <5 shots were hits 
d) Find E[Z] and var[Z] 
e) If the marksman were to get $x for each shot on target.  How much should the marksman expect to get in order to break even on the $10 entry fee?   
7.  Imagine that a vacancy in a 1-D crystal is at the left edge of the crystal.  If the vacancy moves left, it will leave the crystal for good.  Assume that the probability of left and right jumps do not change along with the crystal, even at the boundary.  What is the probability that vacancy escapes? Hint: recursive probability 

 

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  • Posted on : April 17th, 2019

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