STATPRO - PMF, E(X), BINOMIAL, HYPERGEOMETRIC, POISSON

Which of the following is a valid probability mass function (pmf)?

•  $p\left(x\right)=\frac{1}{x}\ \ \ ,\ \ \ \ x\ =1,\ 2,\ 3\$  

•  $p\left(x\right)\ =\ \frac{6}{11\left(x-4\right)}\ \ \ \ ,\ \ \ \ x\ =\ 1,\ 2$  

•  $p\left(x\right)=\frac{9}{\left(x+1\right)}\ \ \ \ ,\ \ \ \ x=1,\ 2,\ 3$  

•  $p\left(x\right)=\frac{1}{2}\ \ \ \ ,\ \ \ \ x=1,\ 2$  

Determine the value of c such that the following is a valid probability mass function (pmf) of a discrete random variable X:

 $p\left(x\right)=\frac{2c}{\left(x-1\right)}\ \ \ ,\ \ \ \ x=2,\ 3,\ 4$  

•  $\frac{3}{11}$  

•  $\frac{11}{3}$  

•  $\frac{3}{5}$  

•  $\frac{5}{3}$  

A fair coin is tossed three times. Let X be the number of 'heads' in the first two tosses.

What is the mean (or expected value) of X?

 $\mu=E\left(X\right)=$  _

What is the probability that a waitress will refuse to serve alcoholic beverages to exactly 3 minors if she randomly checks the IDs of 4 among 9 students, 5 of whom are minors?

In order to compute the probability, we define a random variable:

• X = number of minors among the 9 students

• Y = number of minors among the selected 4 students

• U = number of students who will drink alcohol

• V = number of students with IDs being checked

Which of the following will result in a higher expected winning? Assume that you will bet 1 chip.

38 Numbers:

1-36, 0, and 00

• red numbers

  (payout: 1 to 1)

• multiples of 5

  (payout: 5 to 1)

• multiples of 10

  (payout: 12 to 1)

• 0 or 00

  (payout: 18 to 1)

Which best describes a binomial experiment?

• It consists of equiprobable outcomes.

• It consists of identical trials with two outcomes.

• It consists of a fixed number of independent trials and concludes after the first success is observed.

• It consists of a fixed number of independent and identical trials each with two outcomes.

Customers arrive at the checkout counter of a supermarket at an average rate of 6 per hour. To get the probability that at least 5 customers will arrive at this checkout counter during a 30-minute period, the parameter of a Poisson distribution should be ____.

•  $\mu=12$  

•  $\mu=5$  

•  $\mu=3$  

•  $\mu=30$  

A company needs to hire two from the 5 male and 7 female applicants. No preference is given for choosing either gender. Let X be the number of female applicants chosen to fill the two positions.

What is the probability distribution of X?

• Binomial

• Hypergeometric

• Poisson

A company needs to hire two from the 5 male and 7 female applicants. No preference is given for choosing either gender. Let Y be the number of male applicants chosen to fill the two positions.

Write the probability distribution of Y.

• Y ~ Hypergeometric (N=12, K=7, n=5)

• Y ~ Hypergeometric (N=5, K=2, n=2)

• Y ~ Hypergeometric (N=12, K=5, n=2)

• Y ~ Hypergeometric (N=12, K=7, n=2)

A defective airport metal detector catches a person with metal 80% of the time. Assume independence of people carrying metal.

What is the probability that in a group of 50 people, 40 to 42 persons will be caught with metal? (Round off to FOUR decimal places)