Question

Problem 1: Relations among Useful Discrete Probability
Distributions. A **Bernoulli experiment** consists of
only one trial with two outcomes (success/failure) with probability
of success p. The Bernoulli distribution

is

**P (X = k) =
p**^{k}**q**^{1-k}**,
k=0,1**

The sum of n independent Bernoulli trials forms a binomial
experiment with parameters n and p. The binomial probability
distribution provides a simple, easy-to-compute approximation with
reasonable accuracy to hypergeometric distribution with parameters
N, M and n when n/N is less than or equal to 0.10. In this case, we
can approximate the hypergeometric probabilities by a binomial
distribution with parameters n and p = M/N. Further, the
**Poisson distribution** with mean μ = np gives an
accurate approximation to binomial probabilities when n is large
and p is small.

This is my third time posting this question the first two times
the same person answered it I would like a different person to
answer this time so **if you have already answered this
question please do not answer it again.**

**1. Suppose in a region in Saskatchewan, among a group of
20 adults with cancer, seven were physically abused during their
childhood. A random sample of five adult persons is taken from this
group. Assume that sampling occurs without replacement, and the
random variable X represents the number of adults in the sample who
were abused during their childhood period.**

**(a) Write the formula for p(x), the probability
distribution of X. How this distribution is called?**

**(b) Using the adequate formulas, find the mean and
variance of X?**

**(c) Find the probabilities of all the possible values of
X. Plot the histogram of X and try the locate the approximative
value of the mean μ.**

**(d) What is the probability that at least one person was
abused during childhood?**

**Now suppose another survey in British Columbia reveals
that among 180 adults with cancer, only 80 adults were abused in
their childhood. Suppose again that a random sample of five adult
persons is taken from this group without replacement and let denote
by Y the random variable which represents the number of adults
abused during their childhood period in the sample.**

**(e) Find the probabilities of all the possible values of
Y and plot the histogram of Y. How do you compare this histogram
with the histogram of X.**

**(f) Find the probabilities of all the possible values of
Y using the formula for the binomial distribution with p =
80/180**

**as an approximation. Plot the histogram and compare it
with the histogram obtained using the hypergeometric
formula.**

**(g) Is the precedent approximation close enough? Why or
why not?**

**(h) Calculate the mean and variance using both binomial
and hypergeometric distributions, respectively. Provide a
comparison and summarize your findings**

Answer #1

A biased coin (one that is not evenly balanced) is tossed 6 times.
The probability of Heads on any toss is
0.3. Let X denote the number of Heads that come up.
1. Does this experiment meet the requirements to be considered a
Bernoulli Trial? Explain why or why
not.
2. If we call Heads a success, what would be the parameters of the
binomial distribution of X?
(Translation: find the values of n and p)
3. What is the...

1. Compute the mean and variance of the following probability
distribution. (Round your answers to 2 decimal
places.)
x
P(x)
4
0.10
7
0.25
10
0.30
13
0.35
2. Given a binomial distribution with n = 6 and π=
.25. Determine the probabilities of the following events using the
binomial formula. (Round your answers to 4 decimal
places.)
x = 2
x = 3
3. A probability distribution is a listing of all the outcomes
of an experiment and the...

Question 1 of 3 Which of the following is true about the
random variables X, Y, and Z?
X is binomial with n = 20 and p = .22.
Y is binomial with n = 40 and p = .32.
Z is not binomial. All of the above are true.
Only (A) and (B) are true.
Question 2 of 3 What is the probability that exactly 2
of the 20 older adults prefer organic? (Note: Some answers are
rounded.)
.105...

I. Solve the following problem:
For the following data:
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6 n = 12
b) Calculate
1) the average or average
2) quartile-1
3) quartile-2 or medium
4) quartile-3
5) Draw box diagram (Box & Wisker)
II. PROBABILITY
1. Answer the questions using the following
contingency table, which collects the results of a study to 400
customers of a store where you want to analyze the payment
method.
_______B__________BC_____
A...

Some of the methods in this section are approximations rather
than exact probability results. We have given rules of thumb for
safe use of these approximations. (a) You are interested in
attitudes toward drinking among the 75 members of a fraternity. You
choose 30 members at random to interview. One question is "Have you
had five or more drinks at one time during the last week?" Suppose
that in fact 30% of the 75 members would say "Yes." Explain why...

1.The sample mean is an unbiased estimator for
the population mean. This means:
The sample mean always equals the population mean.
The average sample mean, over all possible samples, equals the
population mean.
The sample mean will only vary a little from the population
mean.
The sample mean has a normal distribution.
2.Which of the following statements is
CORRECTabout the sampling distribution of the
sample mean:
The standard error of the sample mean will decrease as the
sample size increases....

MATHEMATICS
1. The measure of location which is the most likely to
be
influenced by extreme values in the data set is the a. range
b.
median c. mode d. mean
2. If two events are independent, then a. they must be
mutually
exclusive b. the sum of their probabilities must be equal to one
c.
their intersection must be zero d. None of these alternatives
is
correct. any value between 0 to 1
3. Two events, A and B,...

1. What is an ISP (Integrated Service Provider) for supply
chains? (1 point)
A. A consultant agency which integrates the supply chain for
companies
B. A 2 PL or a 3PL, but not a 4PL
C. A company supplying transportation and warehousing
services
D. A logistics service company specialized in suppling VAS (value
added
services)
2. What characterizes a 4 PL? (1 point)
A. They are non-asset based and provides integrated services
primarily
supplied by asset based providers, for example...

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