Question

For each of the following say whether it is a random variable. If yes, write its probability mass function.

(a) the number of double sixes when rolling two fair dice 24 times.

(b) the number of correct questions in an exam with 8 true or false questions by a student who answers all questions at random.

(c) the number of orange marbles in a simple random sample of 5 marbles from an urn that contains 20 blue and 40 orange marbles.

(d) the number of orange marbles in 7 draws with replacement from an urn that contains 20 blue and 40 orange marbles.

(e) the number of red marbles in a simple random sample of 6 marbles from an urn that contains 20 red, 30 green, 40 yellow, 50 blue marbles.

(f) the number of red marbles in 8 draws with replacement from an urn that contains 20 red, 30 green, 40 yellow, 50 blue marbles.

Answer #1

First
Understands,A **random variable** is a
**variable** whose value is a numerical outcome of a
**random** phenomenon.

Out of six statements all comes under random experiment as chances of occurring of events are same and random.

Exercise 8.28 We have an urn with 25 yellow, 30 green and 40 red
marbles. We take a sample of 10 without replacement and denote the
number of yellow and green marbles in the sample by X and Y,
respectively. Find E(X-Y).

Which of the following variables follow binomial distribution?
I. 5% drivers in Winnipeg drive under the influence of alcohol on
Saturdays. 20 drivers are stopped randomly and are asked to take
alcohol test. X = number of drivers who test positive for alcohol.
II. Two bags, A and B contain marbles. Bag A contains 40 red, 30
blue and 30 yellow marbles. Bag B contains 20 red, 10 blue and 20
yellow marbles. A marble is selected from each bag....

Suppose that a drawer contains 8 marbles: 2 are red, 2 are blue,
2 are green, and 2 are yellow. The marbles are rolling around in a
drawer, so that all possibilities are equally likely when they are
drawn. Alice chooses 2 marbles without replacement, and then Bob
also chooses 2 marbles without replacement. Let Y denote the number
of red marbles that Alice gets, and let X denote the number of red
marbles that Bob gets.
8a. Find E(X...

Suppose that a drawer contains 8 marbles: 2 are red, 2 are blue,
2 are green, and 2 are yellow. The marbles are rolling around in a
drawer, so that all possibilities are equally likely when they are
drawn. Alice selects marbles (without replacement) until she gets a
red marble, and then she stops afterwards. Let X denote the number
of draws that are needed until the first red appears.
a. Find P(X=1).?
b. Find P(X=2).?
c. Find P(X=3).?
d....

**ASAP**
A bag contains 7yellow marbles, 10 red marbles, 6 green marbles.
If one marble is drawn from the bag then replaced, what is the
probability of drawing a yellow marble then a green marble?
In a number guessing game. You ask a person to guess a number from
one 1 to 10. If the person makes a random guess, what is the
probability their guess will be less than 8?
A bag contains 10 blue marbles, 6...

Question 1
Mark this question
John makes random guesses on his multiple-choice test, which has
five options for each question. Let the random variable X be the
number of guesses taken before guessing correctly.
Assuming the guesses are independent, find the probability that
he doesn't guess correctly until his 6th guess.
0.0655
0.0789
0.3521
0.3277
Question 2
Mark this question
For a math assignment, Jane has to roll a set of six standard
dice and record the results of each...

An urn contains ten marbles, of which 4 are green, 3 are blue,
and 3 are red. Three marbles are to be drawn from the urn, one at a
time without replacement.
(a) Let ?? be the event that the ?th marble drawn is green. Find
?(?1 ∩ ?2 ∩ ?3), which is the probability that all three marbles
drawn are green. Hint: Use the Multiplicative Law of
Probability
(b) Now let ?? be the random variable defined to be...

________I. Which of the following is an example of a discrete
random variable?
The weight of a box of cookies
The length of a window frame
The number of houses in a development
The distance from home to school
________II. The following table shows the population probability
distribution of x, the random variable representing the price per
ticket, in dollars, for 20 upcoming concerts at a certain
community’s civic center.
Price
per ticket
($)
P(x)
45
0.20...

From an urn that contains only 7 orange balls and 3 blue balls,
take a random sample of 2 balls without replacement. Let the random
variable X be the number of orange balls in the sample. Find P(X =
0). Give your answer to 4 decimal places.

Choose one of the following games from the Games Fair:
Four Coin Flip
Each flip of the four coins costs 10 points
You win:
10 points if you flip two heads
30 points if you flip no heads
Five Card Shuffler
Each hand of five cards costs 10 points
You win:
20 points for no hearts
0 points for one heart
10 points for two hearts
20 points for three hearts
50 points for four hearts
1000 points for five...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 12 minutes ago

asked 42 minutes ago

asked 48 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago