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

1.

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

a)

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

b)

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

c)

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

d)

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

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

a)

$\frac{3}{11}$

b)

$\frac{11}{3}$

c)

$\frac{3}{5}$

d)

$\frac{5}{3}$

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?

$\mu=E\left(X\right)=$ _

(a)

4.

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:

a)

X = number of minors among the 9 students

b)

Y = number of minors among the selected 4 students

c)

U = number of students who will drink alcohol

d)

V = number of students with IDs being checked

5.

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

a)

red numbers

(payout: 1 to 1)

b)

multiples of 5

(payout: 5 to 1)

c)

multiples of 10

(payout: 12 to 1)

d)

0 or 00

(payout: 18 to 1)

6.

Which best describes a binomial experiment?

a)

It consists of equiprobable outcomes.

b)

It consists of identical trials with two outcomes.

c)

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

d)

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

7.

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 ____.

a)

$\mu=12$

b)

$\mu=5$

c)

$\mu=3$

d)

$\mu=30$

8.

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?

a)

Binomial

b)

Hypergeometric

c)

Poisson

9.

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.

a)

Y ~ Hypergeometric (N=12, K=7, n=5)

b)

Y ~ Hypergeometric (N=5, K=2, n=2)

c)

Y ~ Hypergeometric (N=12, K=5, n=2)

d)

Y ~ Hypergeometric (N=12, K=7, n=2)

10.

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)

(a)

11.

The complaints line of a network service provider receives a mean of 8 calls per hour.

What is the probability that in 15 minutes, there are more than 2 calls? (Round off to FOUR decimal places)

(a)

12.

A company shipped 30 smartphones to an online reseller. Later, it found out that 10 of those smartphones were defective. If 7 smartphones from that shipment had already been sold by the online reseller, what is the probability that at most 5 of those 7 smartphones were not defective? (Round off to FOUR decimal places)

(a)

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

Total questions: 12

Worksheet time: 17mins

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