Tag: Probability

Probability

Posted on | by Brian Leakey

Consider the population described by the probability dis-tribution shown below.

x p1x2

1 2 3 4 5 .3

.2 .2 .2 .1

The random variable x is observed twice. If these observa-tions are independent, verify that the different samples of size 2 and their probabilities are as shown below.

Sample Probability 1, 1

1, 2 1, 3 1, 4 1, 5 2, 1 2, 2 2, 3 2, 4 2, 5 3, 1 3, 2 3, 3

.04 .06 .04 .04 .02 .06 .09 .06 .06 .03 .04 .06 .04

Sample Probability 3, 4

3, 5 4, 1 4, 2 4, 3 4, 4 4, 5 5, 1 5, 2 5, 3 5, 4 5, 5

.04 .02 .04 .06 .04 .04 .02 .02 .03 .02 .02 .01

5.4 Refer to Exercise 5.3 and find E1x2 = m. Then use the sampling distribution of x found in Exercise 5.3 to find the expected value of x. Note that E1x2 = m.

5.5 Refer to Exercise 5.3. Assume that a random sample of n = 2 measurements is randomly selected from the population.

a. List the different values that the sample median m may assume and find the probability of each. Then give the sampling distribution of the sample median.

b. Construct a probability histogram for the sampling distribution of the sample median and compare it with the probability histogram for the sample mean (Exercise 5.3, part b).

Probability

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Design a lesson plan and presentation on one of the subjects from below.

Topic 1 Probability

Topic 2 Data Analysis and statistics

Topic 3 Introductory Geometry

Topic 4 Congruence and Similarity with Constructions

Topic 5 Congruence and Similarity with Transformations

Topic 6 Area, Pythagorean Theorem, Volume

Include the following:

Overview: Write an introduction to the class activity. Include the purpose of the activity and desired outcome.
Objectives: The objectives should be specific and measurable.
Time: How long will the activity take when implemented in the classroom?
Materials: Describe any materials that are needed to conduct the lesson.
Activity: Provide a detailed description of the activity. Write all steps from the instruction of the assessment.
Presentation: Complete a PowerPoint presentation that could be used in class to teach the lesson plan.
Notes: The PowerPoint should include presentation notes.

Probability

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 Suppose you go out for pizza with two friends. You have agreed to the following rule to decide who
will pay the bill. Each person will toss a coin. The person who gets a result that is diGGerent from the other
two will pay the bill. If all three tosses yield the same result, the bill will be shared by all.
B
List the sample space. (Hint: What are the possible combinations of the coin toss?)
C
Find the probability that only you will have to pay.
D
Find the probability that all three will share the expense.
 Suppose “BOE#BSF UXP FWFOUT TVDI UIBU
P(A)=.50 and P(B)=.22. Answer the following questions.
(a) Determine P(A S B) if A and B are independent.
(b) Determine P(A S B) if A and B are mutually exclusive.
. Let X be a random variable that represents the number of students who are absent on a given day from a
class of 25. The following table lists the probability distribution of X.
x 012345
P(x) .08 .18 .32 .22 .14 .06
(a) Determine the following probabilities. P(X = 4), P(X > 4), P(2 < X  4), and P(X 1).
(b) Determine the expected number of absent students on a given day.
(c) Compute the variance of X by definition.
 According to the Mendelian theory of inherited characteristics, a cross fertilization of related spices of red
and yellow flowered plants produces a generation whose oGGTpring contain 25% red-flowered plants. Suppose
that a horticulturist wishes to cross 5 pairs of the cross-fertilized species.
B
Justify that each cross fertilization of the red- and yellow-flowered plants is a Bernoulli trial.
Let X be the number of red-flowered plants in 5 pairs of the cross-fertilized species.
C
Is X a binomial random variable? If Yes, identify n and p.
D
Determine the probability that there will be no red-flowered plant.
E
Determine the probability that there will be at least one red-flowered plant.
F
Determine E(X), V ar(X) and SD(X). (Hint:not necessary to compute through the definition of mean
and variance.)
(d) Determine the standard deviation of X.
 Z is a standard normal random variable. Determine the following probabilities.
B
P (0 < Z < 1.96), P (Z < 1.96), and P (Z < 1.96).
C
P (1.5 < Z < 2), and P (1.5 < Z < 2).
D
P (1 < Z < 1), P (2 < Z < 2), and P (3 < Z < 3). Compare these probabilities to those in the
empirical rule.