Asked Jul 8, 2019

I asked the attached question earlier today, and a response was sent, but none of the answer appeared.  It shows the green check mark as if it has been answered, but nothing followed.

Let X(n, p) denote a binomial random variable with parameters n and p. If
P1 P2, show that X(n, p) st X(n, p2)

Image Transcriptionclose

Let X(n, p) denote a binomial random variable with parameters n and p. If P1 P2, show that X(n, p) st X(n, p2)


Expert Answer

Step 1

Introduction to binomial distribution:

Consider a random experiment involving n independent trials, such that the outcome of each trial can be classified as either a “success” or a “failure”. The numerical value “1” is assigned to each success and “0” is assigned to each failure.

Moreover, the probability of getting a success in each trial, p, remains a constant for all the n trials. Denote the probability of failure as q. As success and failure are mutually exclusive, q = 1 – p.

Let the random variable X denote the number of successes obtained from the n trials. Thus, X can take any of the values 0,1,2,…,n.

Then, the probability distribution of X is a Binomial distribution with parameters (n, p) and the probability mass function (pmf) of X, that is, of a Binomial random variable, is given as:


Image Transcriptionclose

piq*, x 0,1.,n;0 < p< 1;q=1-p P(x) [0, otherwise.

Step 2

Given information:

Here, it is given that X(n,p) is a binomial random variable with parameters n and p.

Consider a binomial random variable X1= X(n,p1).

Consider another binomial random variable X2= X(n,p2).

If X(n,p) is a binomial random variable, then the mean and variance for the binomial variate X are E(x) = n * p and V(x) = n *p *(1 – p).

Since, X1 is a binomial random variable with parameters n and p1, the mean of the binomial random variable X1 is E(X1) = np1.

Since, X2 is a binomial random variable with parameters n and p2, the mean of the binomial random variable X2 is E(X2) = np2.

Step 3

Calculation to show that X(n,p1) ≥st X(n,p2):

From the below given calculation, it is proved that X(n,p1) ≥st X(n,p2):


Image Transcriptionclose

To show that, X(n, p1)X(n,p) :X- В(п,р.) х, ~ в (п, р,) and It is enough to show that, E(X2 E(X It is known that E(X =np and E (X) = np From the given information, it is known that, p 2 p, duz du That is, E(X) E(X2) X(п, р.)2 X (п,р,) Hence proved


Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in




Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Intelligence quotas on two different tests are normally distributed. Test A has a mean of 100 and a ...

A: In this question, it has been given that two different tests A and B are normally distributed, Test ...


Q: A study was conducted to see whether participants would ignore a sign that said, "Elevator may stick...

A: Explanation:Here, the experimenter controls the presence/absence of the confederates, as its effect ...


Q: A random sample of 30 binomial trials resulted in 12 success. Test the claim that the population por...

A:  Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three s...


Q: In a recent survey it was stated that Americans watch television on average four hours per day. Assu...

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...


Q: Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of who...

A: (A)The sample mean and standard deviation is calculated below:


Q: 9.3 Question is in the attached picture.

A: a. Identifying whether the linear combination are contrast:Contrast:A contrast is linear combination...


Q: A group says that the mean daily lodging cost for a family traveling in Region 1 is the same as in R...

A: Given the data of mean daily lodging cost for a family traveling in Region 1 and Region 2.The claim ...


Q: The Orchard Cafe has found that about 10% of the diners who make reservations don't show up. If 86 r...

A: Binomial distribution:A random variable X follows binomial distribution if it follows the given prop...


Q: Suppose that from the past experience a professor knows that the test score of a student taking his ...

A: If a random variable X has a distribution with mean µ and standard deviation σ, then the Z-score is ...