3. Buses arrive to a bus stop according to an exponential distribution with rate

?= 4 busses/hour. If you arrived at 8:00 am to the bus stop,

a) what is the expected time of the next bus?

b) Assume you asked one of the people waiting for the bus about the arrival

time of the last bus and he told you that the last bus left at 7:40 am. What

is the expected time of the next bus?

4. Break downs occur on an old car with rate ?= 5 break-downs/month. The owner

of the car is planning to have a trip on his car for 4 days.

a) What is the probability that he will return home safely on his car.

b) If the car broke down the second day of the trip and the car was fixed, what is

the probability that he doesn't return home safely on his car.

5. Suppose that the amount of time one spends in a bank is exponentially distributed with

mean 10 minutes. What is the probability that a customer will spend more than 15

minutes in the bank? What is the probability that a customer will spend more than 15

minutes in the bank given that he is still in the bank after 10 minutes?

6. Suppose the lifespan in hundreds of hours, T, of a light bulb of a home lamp is

exponentially distributed with lambda = 0.2. compute the probability that the light bulb

will last more than 700 hours Also, the probability that the light bulb will last more than

900 hours

7. Let X = amount of time (in minutes) a postal clerk spends with his/her customer. The

time is known to have an exponential distribution with the average amount of time equal

to 4 minutes.

a) Find the probability that a clerk spends four to five minutes with a randomly selected

customer.

b) Half of all customers are finished within how long? (Find median)

c) Which is larger, the mean or the median?

8. On the average, a certain computer part lasts 10 years. The length of time the computer

part lasts is exponentially distributed.

a) What is the probability that a computer part lasts more than 7 years?

b) On the average, how long would 5 computer parts last if they are used one after

another?

c) Eighty percent of computer parts last at most how long?

d) What is the probability that a computer part lasts between 9 and 11 years?

9. Suppose that the length of a phone call, in minutes, is an exponential random variable

with decay parameter = 1/12 . If another person arrives at a public telephone just before

you, find the probability that you will have to wait more than 5 minutes. Let X = the

length of a phone call, in minutes. What is median mean and standard deviation of X?

1. Calculate the Poisson distribution whose ? (Average Rate of Success)) is 3 & X (Poisson

Random Variable) is 6.

2. Customers arrive at a checkout counter according to a Poisson distribution at an average

of 7 per hour. During a given hour, what are the probabilities that

a) No more than 3 customers arrive?

b) At least 2 customers arrive?

c) Exactly 5 customers arrive?

3. Manufacturer of television set knows that on an average 5% of their product is defective.

They sells television sets in consignment of 100 and guarantees that not more than 2 set

will be defective. What is the probability that the TV set will fail to meet the guaranteed

quality?

4. It is known from the past experience that in a certain plant there are on the average of 4

industrial accidents per month. Find the probability that in a given year will be less that 3

accidents.

5. Suppose that the change of an individual coal miner being killed in a mining accident

during a year is 1.1499. Use the Poisson distribution to calculate the probability that in

the mine employing 350 miners- there will be at least one accident in a year.

6. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 3. Find the probability that exactly five road

construction projects are currently taking place in this city. (0.100819)

7. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 7. Find the probability that more than four

road construction projects are currently taking place in the city. (0.827008)

standard deviation of the mean. 39. Demand The daily demand x for a certain product (in hundreds of pounds) is a random variable with the probability density function f ( x ) = 6 343 x(7 - x), [0, 7]. (a) Find the mean and standard deviation of the demand. (b) Find the median of the demand. (c) Find the probability that the demand is within one standard deviation of the mean. warnica 20 for the probabilityEEE 304, Communication System I, Spring 2018 (Deadline: 27.03.2018) - 263.2018 mert . comer 10.00- 12.00 pm / @stu.HALL Generation of random sequences: While deterministic signals such as square pulses, sinc Soft waveforms, sinuses and cosines are used in specific applications, almost all other real-life NO+ 10 signals from econometric series to radar returns, from genetic codes to multimedia signals in cost consumer electronics are information-bearing random signals. re Time sequences: Generate a sequence of 1000 equally spaced samples of a Gauss- - je Markov process using the recursive relation: Xn = axn-1+ Win = 1,2, ..., 1000. Here ab int assume that X0 = 0, and {w,) is a sequence of independent identically distributed Gaussian random variables. You can use the randn function in MATLAB to generate re zero-mean, unit-variance random variables. Below is given a low-pass filter (a>0) excited by a white noise sequence, and the filter has a real pole at z- a. Plot the output waveform for the following values of a: a= 0.5, a = 0.95, a = 0.995. Comment on the effect of the selection of a on the resulting time sequence.For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. x [0. 2] 0 1-4:02- 4:0-24 For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 1(x) - 4. [2 25. 2.50] Q u - 2.500; 02 - 0.0049 0 = 0.070 Q u - 2375; 02- 0.0052: 0 - 0.072 1 - 2.375, 03 - 0.021; 0 = 0.144 HI - 2.500 02 = 0.0048: 0 - 0.069 For the given probability density function, over the stated interval, find the requested value. * over the interval [0.3]. Find E(x 2), O 16 O 20 Let x be a continuous random variable with a standard normal distribution. Find the requested probability. P(1.26 x x x 2.15] 0.0898 0 0.088 O 0.0862 O 0.588 Find k such that the function is a probability density function over the given interval. Then write the probability dentity function. f(x) = k(11 - x* [0. 11] 121: 160 - 121(11-x THE : fix) " Ty (1 1 .x) O 11: 61x) = 1101 1 - x)Regression Equation in Uncoded Units RESPONSE = 5.839 - 1.345 A/C - 0.096 TR/PA + 0.0868 TI/PR + 0.400 A/C.TR/PA + 0.0189 A/C.TI/PR - 0.0200 TR/PA"TI/PR - 0.0120 A/C*TR/PA*TI/PR Regression Equation in Uncoded Units Response = 9.35 - 2.07 A/C + 0.16 TR/PA + 0.2228 TI/PR . 1.86 A/C'TR/PA . 0.0144 A/C . 0.0519 TR/PA'TV/PR . 0.0544 A/C*TR/PA*TV/PR i want an explination about the numbers in the reggression model our response is kilometer per liter we are studying the affect on the fuel our factor is AC: air conditioning TR/PA: traffic pattren TI/PR: tire pressure 2 cars GMC YOKUN and toyota corolla