## Description

Part1) Binomial distribution (20 points)

Suppose a pitcher in Baseball has 50% chance of getting a strike-out when

throwing to a batter. Using the binomial distribution,

a) Compute and plot the probability distribution for striking out the next 6

batters.

b) Plot the CDF for the above

c) Repeat a) and b) if the pitcher has 70% chance of getting a strike-out.

d) Repeat a) and b) if the pitcher has 30% chance of getting a strike-out.

e) Infer from the shape of the distributions.

Part2) Binomial distribution (15 points)

Suppose that 80% of the flights arrive on time. Using the binomial

distribution,

a) What is the probability that four flights will arrive on time in the next 10

flights?

b) What is the probability that four or fewer flights will arrive on time in the

next 10 flights?

c) Compute the probability distribution for flight arriving in time for the next

10 flights.

d) Show the PMF and the CDF for the next 10 flights.

Part3) Poisson distribution (15 points)

Suppose that on average 10 cars drive up to the teller window at your bank

between 3 PM and 4 PM and the random variable has a Poisson

distribution. During this time period,

a) What is the probability of serving exactly 3 cars?

b) What is the probability of serving at least 3 cars?

c) What is the probability of serving between 2 and 5 cars (inclusive)?

d) Calculate and plot the PMF for the first 20 cars.

Part4) Uniform distribution (15 points)

Suppose that your exams are graded using a uniform distribution between

60 and 100 (both inclusive).

a) What is the probability of scoring i) 60? ii) 80? iii) 100?

b) What is the mean and standard deviation of this distribution?

c) What is the probability of getting a score of at most 70?

d) What is the probability of getting a score greater than 80 (use the

lower.tail option)?

e) What is the probability of getting a score between 90 and 100 (both

inclusive)?

Part5) Normal distribution (20 points)

Suppose that visitors at a theme park spend an average of $100 on

souvenirs. Assume that the money spent is normally distributed with a

standard deviation of $10.

a) Show the PDF plot of this distribution covering the three standard

deviations on either side of the mean.

b) What is the probability that a randomly selected visitor will spend more

than $120?

c) What is the probability that a randomly selected visitor will spend

between $80 and $90 (inclusive)?

d) What are the probabilities of spending within one standard deviation, two

standard deviations, and three standard deviations, respectively?

e) Between what two values will the middle 90% of the money spent will

fall?

f) Show a plot for 10,000 visitors using the above distribution.

Part6) Exponential distribution (15 points)

Suppose your cell phone provider’s customer support receives calls at the

rate of 18 per hour.

a) What is the probability that the next call will arrive within 2 minutes?

b) What is the probability that the next call will arrive within 5 minutes?

c) What is the probability that the next call will arrive between 2 minutes

and 5 minutes (both inclusive)?

d) Show the CDF of this distribution.

Submission:

Create a folder, CS544_HW4_lastName and place the following file in this

folder.

Provide the R code, HW4_lastName.R, with each portion of the code

clearly identified by the corresponding question. Prepare a corresponding

word document by pasting the output for each question

(HW4_lastName.docx)

Archive the folder (CS544_HW4_lastName.zip). Upload the zip file to

the Assignments section of Blackboard.