Business
Engineering
Math
Science
Social ScienceLet X(n, p) denote a binomial random variable with parameters n and p. IfP1 P2, show that X(n, p) st X(n, p2)
See the attached question.
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
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
п |P'a*, х%3D0,1,..7:0 <p<1;q%31-р Р(3) -{ х otherwise [0,
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.
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(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
Math
Statistics
Other
Related Statistics Q&A
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 ...
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. ...
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 ...
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 ...
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...
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 ...
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...
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...
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:
