Statistics and Probability Answers

An internet service provider has given you the following data to consider:

Year 1999 2000 2001 2002 2003 2004 2005 2006

Customers

(in

millions)

76.4 78.6 81.5 87.8 88.4 92.4 94.0 95.0

Use MATLAB to plot the data and observe its trend. Find a liner function for the data and use

it to predict the number of customers the company will have in 2014.

Define sample, population, variable, stem-and-leaf with example.

Probability function of the random variable X is:

f(x)=k/2^x , x = 0,1,2.......

a. Compute k.

b. Compute P(X ≥ 6).

c. Compute P(1 ≤ X ≤ 6).

20% of people are vegetarians. 70% of vegetarians like broccoli. 20% of vegetarians like

carrot. 10% of vegetarians like cucumber. 40% of meat eaters like broccoli. 60% of meat

eaters like carrot. What is the probability that a man who likes carrot is a meat eater?

Let X be a Bernoulli random variable (Hint: Special case of Binomial

Distribution)

a. Compute E(X²)

b. Show that V(X) is p(1 − p).

c. Compute E(X⁷⁹)

An insurance company offers its policyholders a number of different premium payment

options. For a randomly selected policyholder, let X = number of months between

successive payments. The cdf of X is as follows:

0  x < 1

0.30 1 ≤ x< 3

f(x)= 0.40 3 ≤ x < 4

0. 45 4 ≤ x < 6

0.60 6 ≤ x ≤ 12

1 12 ≤ x .

a) What is the pmf of X ?

b) Using just the cdf, compute P(3 ≤ X ≤ 6) and P(4 ≤ X).

Consider randomly selecting a single individual and having that person test

drive 3 different vehicles. Define events A1, A2, and A3 by A1=likes vehicle #1,

A2 =likes vehicle #2, A3 =likes vehicle #3. Suppose that ( ) 65.0 P A1 = ,

( ) 55.0 P A2 = , ( ) 70.0 P A3 = , ( ) 80.0 P A1 ∪ A2 = , ( ) ,60.0 P A1 ∪ A3 = ( ) 40.0 P A2 ∪ A3 = ,

( ) 88.0 P A1 ∪ A2 ∪ A3 = .

a. What is the probability that the individual likes both vehicle #1 and vehicle #3?

b. Determine and interpret ( / ) P A1 A3.

c. Are A1 and A2 independent events? Answer in two different ways.

d. If you learn that the individual did not like vehicle #2, what now is the

probability that he/she liked at least one of the other two vehicles

y=-0.0575x+7.3

Find the variance of the r.v. whose m.g.f is (𝑒^−𝑡)/12(2+𝑒^𝑡+6𝑒^3𝑡+3𝑒^6𝑡)