Suppose that we observe a random variable having the binomial distribution. Let (X) be the number of

Question:

Suppose that we observe a random variable having the binomial distribution. Let $X$ be the number of successes in $n$ trials.

(a) Show that $\frac{X}{n}$ is an unbiased estimate of the binomial parameter $p$.

(b) Show that $\frac{X+1}{n+2}$ is not an unbiased estimate of binomial parameter $p$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability And Statistics For Engineers

ISBN: 9780134435688

9th Global Edition

Authors: Richard Johnson, Irwin Miller, John Freund

See More Books

Question Posted: Apr 23, 2024 07:01 AM

See More Questions

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...
The number of successes in n trials is to be used to test the null hypothesis that the parameter Î¸ of a binomial population equals 12 against the alternative that it does not equal 12....
Suppose a city finds that its express highways into the city are congested and it is considering two remedies: (1) imposing a congestion charge on all users of its expressways during the peak periods...
The following bond investment transactions were completed during 2016 by Starks Company: Jan. 31. Purchased 75, $1,000 government bonds at 100 plus 30 days' accrued interest. The bonds pay 6% annual...
The motion of pin P is guided by slots cut in rods AE and BD. Knowing that the rods rotate with the constant angular velocities A = 4 rad/s clockwise and B = 5 rad/s clockwise, determine the velocity...
The PFD in Figure 11.63 shows a process in which two liquid products, A and B, are produced from a feed stream of raw material R. In the process, the reactor feed is preheated to \(300^{\circ}...
CommercialServices.com Corporation provides business-to-business services on the Internet. Data concerning the most recent year appear below: Sales . . . . . . . . . . . . . . . . . . . . . . . . . ....
Selling price Variable expenses Contribution margin . Per Unit of Sales $ 80 52 100% 65 $ 28 35% Fixed expenses are $76,000 per month and the company is selling 4,600 units per month. Exercise 6-5...
The statistical program MINITAB will calculate the small sample confidence interval for $\mu$. With the nanopillar height data in $\mathrm{C} 1$, produces the output (a) Obtain a $90 \%$...
Instead of the large sample confidence interval formula for $\mu$ on page 230, we could have given the alternative formula \[\bar{x}-z_{\alpha / 3} \cdot \frac{\sigma}{\sqrt{n}} Explain why the one...
(a) Suppose you prepare 500 mL of a 0.10 M solution of some salt and then spill some of it. What happens to the concentration of the solution left in the container? (b) Suppose you prepare 500 mL of...
In the capitalist system, the profits generated by a firm belong to: those who own the firm's capital those who work in the firm those who own the land where the firm is located those who sell inputs...
A leaky 15-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.9 kg/m. Initially the bucket contains 30 kg of water, but the water leaks at a...
The simplico gold mine has a great deal of remaining gold deposits, and you are part of a team that is considering leasing the mine from its owners for a period of 1 0 years. Gold can be extracted...
Highly Suspect Corporation has current liabilities of $412,000, a quick ratio of 1.50, inventory turnover of 4.10, and a current ratio of 3.20. What is the cost of goods sold for the company?
Choose the riskiest position to take in the stock index options market if the stock market is expected to increase after you finalize the transaction. A . Buy a put option B. Buy a call option C....
Devise an ideal regenerative Rankine cycle that has the same thermal efficiency as the Carnot cycle. Show the cycle on a T-s diagram
The manager for retail customers, Katie White, wants to hear your opinion regarding one business offer she has received from an entrepreneur who is starting a mobile phone app called Easy Money. The...
The furnace is at 750 F and the convective heat transfer coefficient inside and outside of the furnace are 40 and 10 Btu/ft 2 .F.hr respectively. To evaluate the warm-up time of the furnace, assume...
1. Calculate the Stiffness of the foam (assume linear) 2. Calculate the Damping ratio Use the results below: Period =11f= 1 / 4 = .25 Frequency = 11t= 1/.25 = 4 Angular frequency = 22t= 2f = 25.12
A closed - tube barometer has a height of 6 6 4 mm when placed in a room at . 8 8 atm ( recall 1 atm = 1 . 0 1 x 1 0 5 N / m 2 ) of pressure. If mercury has a density of 1 3 , 6 0 0 kg / m 3 , how...

Suppose that we observe a random variable having the binomial distribution. Let (X) be the number of

Question:

Step by Step Answer:

SOLUTION a We are given that X Binomialn p To show ...View the full answer

Probability And Statistics For Engineers

Students also viewed these Business questions