Question

- Develop an algorithm for generation a random sample of size
*N*from a binomial random variable*X*with the parameter*n, p*.

[**Hint:** *X* can
be represented as the number of successes in *n* independent
Bernoulli trials. Each success having probability *p,* and
*X =*
*S _{i=1}*

(a) Generate a sample of size
*32* from *X ~ Binomial (n = 7, p = 0.2)*

(b) Compute the sample mean and variance

(c) Make a histogram of the sample of part (a) and compare it
with the theoretical probability density function of
*X.*

Answer #1

Let X be the binomial random variable obtained by adding n=4
Bernoulli Trials, each with probability of success p=0.25. Define
Y=|X-E(x)|. Find the median of Y.
A.0
B.1
C.2
D.3
E.Does not exist

Use R to code a function to generate a random sample of size n
from the Beta(a, b) distribution by the acceptance-rejection
method.
(1) Generate a random sample of size 3000 from the Beta(4,3)
distribution.
(2) Graph the histogram of the sample with the theoretical
Beta(4,3) density superimposed.
Answer the above questions by showing the R codes and
results.

Given a random sample size n=1600 from a binomial probability
distribution with P=0.40 do the following... with probability of
0.20 Find the number of successes is less than how many? Please
show your work

Given a random sample of size of
n equals =3,600
from a binomial probability distribution with
P equals=0.50,
complete parts (a) through (e) below.
Click the icon to view the standard normal table of the
cumulative distribution function
.a. Find the probability that the number of successes is greater
than 1,870.
P(X greater than>1 comma 1,870)
(Round to four decimal places as needed.)b. Find the
probability that the number of successes is fewer than
1 comma 1,765.
P(X less than<1...

Compute the probability of 6 successes in a random sample of
size n=11 obtained from a population of size N=70 that contains 25
successes.
The probability of 6 success is?

Let U be a Standard Uniform random variable. Show all the steps
required to generate:
An exponential random variable with the parameter λ = 3.0;
A Bernoulli random variable with the probability of success
0.65;
A Binomial random variable with parameters n = 12 and p =
0.6;

A
random variable follows a binomial distribution with a probability
of success equal to 0.52. For a sample size of n=7, find the values
below.
a. the probability of exactly 3 successes
b. the probability of 4 or more successes
c. the probability of exactly 7 successes
d. the expected value of the random variable

A random variable follows a binomial distribution with a
probability of success equal to 0.69 For a sample size of N=11,
find the values below.
a. the probability of exactly 3 successes
b. the probability of 7 or more successes
c. the probability of exactly 10 successes
d. the expected value of the random variable

Assume that a procedure yields a binomial distribution with with
n=8 trials and a probability of success of p=0.90. Use a binomial
probability table to find the probability that the number of
successes x is exactly 4.
1. P(4)= ?

Determine if the random variable from the experiment follows a
Binomial Distribution.
A random sample of 5 SLCC professors is obtained, and the
individuals selected are asked to state the number of years they
have been teaching at SLCC.
1. There there are two mutually exclusive outcomes
(success/failure).
[ Select ]
["FALSE",
"TRUE"]
2. Since a sample size of 5 is less than...

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