Question
Asked Jul 8, 2019
32 views

See the attached question.

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)
help_outline

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)

fullscreen
check_circle

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:

help_outline

Image Transcriptionclose

п |P'a*, х%3D0,1,..7:0 <p<1;q%31-р Р(3) -{ х otherwise [0,

fullscreen
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):

...
help_outline

Image Transcriptionclose

To show that, X(п, р.) > X(п,р,) (: X~ в(п, р,) and х, ~ в (п,р,) It is enough to show that, E(X)2 E(X It is known that E(x =np andE(x) = np2 From the given information, it is known that, p 2 p du z du That is, E(X)2 E (X;) х(п,р.) 2 X (п,р.) Hence proved

fullscreen

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

Math

Statistics

Other

Related Statistics Q&A

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

Q: A personnel director in a particular state claims that the mean annual income is the same in one of ...

A: According to the given question, in order to test that the annual income is the same in one of the​ ...

question_answer

Q: The state superintendent of schools consistently states that the average salary of all substitute te...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

question_answer

Q: Listed below are the amounts of mercury​ (in parts per​ million, or​ ppm) found in tuna sushi sample...

A: In this question, we have the data of amount of mercury in tuna sushi stores using the data we have ...

question_answer

Q: How do you calculate a coefficient of correlation of two indexes’ returns?

A: Let the two indexes’ returns be A and B.The coefficient of correlation measures the degree to which ...

question_answer

Q: What happens to the variance when outliers are eliminated replaced by values closer to the mean

A: Introduction:Mean:Mean is an important measure of center when the data is quantitative. Mean of a da...

question_answer

Q: Joe likes to go to an old arcade and play 12 games of Skeeball every day. On​ average, he wins a pri...

A: In this context, there are fixed number of trials. That is, n = 12. There are two possible outcomes ...

question_answer

Q: An economist is studying the job market in Denver area neighborhoods. Let x represent the total numb...

A: Scatter PlotIt is a Graph between two variables. It is plotted to check the relationship between the...

question_answer

Q: If the probability for an event E is P(E)=0.4, then what are the odds against E?

A: Odds against an event:The odds against an event is given by the ratio of the probability of the even...

question_answer

Q: Five children aged 2, 3, 5, 7 and 8 years old weigh 14, 20, 32, 42 and 44 kilograms respectively. Fi...

A: Let x be the age of children and y be the weight of children.The equation of the regression line is: