Question
In: Math
4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock...
4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock drawer with N socks, each placed loosely in the drawer (not rolled into pairs). The total number of black socks is m. You take out a random sample of n < m socks. Assume all the socks are the same shape, size, etc. and that each sock is equally likely to be chosen.
(a) Suppose the sampling is done without replacement. Calculate the probability of getting at least 2 black socks (your goal in order to wear matching black socks that day...) under the following conditions:
(i) N = 10, n = 4, m = 5.
(ii) N = 20, n = 4, m = 10.
(iii) N = 40, n = 4, m = 20.
(b) Suppose the sampling is done with replacement (this doesn’t make much sense if you are planning to wear the socks!). Calculate the probability of getting at least two black socks when you sample four socks and the proportion of black socks is 0.5. Compare your answer to those in (a).
Solutions
milcah answered 5 months agoRelated Solutions
Think about these three probability distributions: hypergeometric, binomial, and Poisson and describe one or more ways...
Think about these three probability distributions:
hypergeometric, binomial, and Poisson and describe one or more ways
that you might use any of these distributions to explore their
applications in different situations that need not be particularly
economically valuable
How can you identify when to use the binomial, geometric and hypergeometric probability distributions? For example,...
How can you identify when to use the binomial, geometric and
hypergeometric probability distributions? For example, if I want to
flip a coin until I get heads, it is geometric, but if I flip the
coin 5 times, it becomes binomial. What changed? How do I know
which distribution to use?
Sock Problem: Your sock drawer is very unorganized! No socks are paired, and they are all...
Sock Problem:
Your sock drawer is very unorganized! No socks are paired, and they
are all just thrown randomly into the drawer. You do know that the
drawer has four red socks and four blue socks in it. You want to
get some socks to wear in the morning, but you do not want to turn
on a light for fear of waking up your family.
If you draw two, what is the probability of a red pair
match?
If...
What is a complex aspect of binomial distributions?
What is a complex aspect of binomial distributions?
Question: Give an example of a hypergeometric random variable for which a binomial random variable is...
Question:
Give an example of a hypergeometric random variable for which a
binomial random variable is NOT a good approximation. You must
describe each of the following:
i. the experiment
ii. a random variable X from the experiment and what X
represents
iii. the probability mass function (PMF) of X
iv. a binomial random variable that approximates X and its
parameters
v. the PMF of the binomial random variable and why it's a good
estimate of the PMF of X
Question 2 Graph P(X=x) for binomial distributions with the following parameters a) ? = 4 ???...
Question 2
Graph P(X=x) for binomial distributions with the following
parameters
a) ? = 4 ??? ? = 0.5
b) ? = 4 ??? ? = 0.3
c) ? = 4 ??? ? = 0.1
d) Which if any of the graphs in part a-c are
symmetric?
e) Without actually constructing the graph, would
the case
? = 10 ??? ? = 0.5 be symmetric or skewed?
f) Which of the graphs in part a-c is the most
heavily skewed?...
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the...
The binomial and Poisson distributions are two different
discrete probability distributions. Explain the differences between
the distributions and provide an example of how they could be used
in your industry or field of study. In replies to peers, discuss
additional differences that have not already been identified and
provide additional examples of how the distributions can be
used.
What is Normal, Binomial, Poisson and Exponential Distributions with examples. What is Continuous Distributions and Density...
What is Normal, Binomial, Poisson and Exponential Distributions
with examples.
What is Continuous Distributions and Density Functions.
What is Normal density and Standardizing: Z-Values
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the...
The binomial and Poisson distributions are two different
discrete probability distributions. Explain the differences between
the distributions and provide an example of how they could be used
in your industry or field of study.
Work the following probability sock problem, keeping in mind that this is a problem without replacement....
Work the following probability sock problem, keeping in mind
that this is a problem without replacement. When you take out a
sock, it stays out.
Sock Problem:
Your sock drawer is very unorganized. No socks are paired, and
they are all just thrown randomly into the drawer. You do know that
the drawer has four red socks and four blue socks in it. You want
to get some socks to wear in the morning, but you do not want to...
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