Question

Let *X* be a binomial random variable with *n* =
400 trials and probability of success *p* = 0.01. Then the
probability distribution of *X* can be approximated by

Select one:

a. a Hypergeometric distribution with *N* =
8000, *n* = 400, *M* = 4.

b. a Poisson distribution with mean 4.

c. an exponential distribution with mean 4.

d. another binomial distribution with *n* =
800, *p* = 0.02

e.

a normal distribution with men 40 and variance 3.96.

Answer #1

We have given that , X follows a Binomial distribution with n= 400 and success probability p=0.01.

We can use a Normal distribution as a limiting distribution of binomial , but when n> 20 and p<= 0.05

That is,when np< 10 , then Poisson approximation to binomial is appropriate.

Here, np = 4 ie , np<10

So, we approximate Binomial to Poisson distribution with mean, = n* p = 400* 0.01 = 4

So correct option is b) a Poisson distribution with mean =4.

Let B~Binomial(n,p) denote a binomially distributed
random variable with n trials and probability of success
p. Show that B / n is a consistent estimator for
p.

Suppose we have a binomial distribution with n trials
and probability of success p. The random variable
r is the number of successes in the n trials, and
the random variable representing the proportion of successes is
p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four...

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

Determine the probability P2 or fewer for a binomial experiment
with n=13 trials and the success probability
p=0.2 Then find the mean, variance, and standard deviation.

A) Suppose we are considering a binomial random variable X with
n trials and probability of success p.
Identify each of the following statements as either TRUE or
FALSE.
a) False or True - The variance is greater than n.
b) False or True - P(X=n)=pn.
c) False or True - Each individual trial can
have one of two possible outcomes.
d) False or True - The largest value a
binomial random variable can take is n + 1.
e)...

Assume the random variable X has a binomial distribution with
the given probability of obtaining success. Find the following
probability, given the number of trials and the probability of
obtaining success. Round your answer to four decimal places.
P(X≥7), n=10, p=0.3

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)= ?

In the binomial probability distribution, let the number of
trials be n = 3, and let the probability of success be p = 0.3742.
Use a calculator to compute the following.
(a) The probability of two successes. (Round your answer to
three decimal places.)
(b) The probability of three successes. (Round your answer to
three decimal places.)
(c) The probability of two or three successes. (Round your
answer to three decimal places.)

Assume that Y is distributed according to a binomial
distribution with n trials and probability p of success.
Let g(p) be the probability of obtaining either no successes or all
successes, out of n trials. Find the MLE
of g(p).

Assume that a procedure yields a binomial distribution with n
trials and the probability of success for one trial is p. Use the
given values of n and p to find the mean μ and standard deviation
σ. Also, use the range rule of thumb to find the minimum usual
value μ−2σ and the maximum usual value μ+2σ.
n=1405, p= 2 / 5

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 12 minutes ago

asked 21 minutes ago

asked 37 minutes ago

asked 58 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago