For four pairs of a rare specimen of bird that nested last season, the number of eggs per nest n and thenumber of eggs hatched Y were observed, providing the datan = 2, 3, 3, and 4 and y = 1, 2, 3 and 3.Let T be the probability that an egg is hatched. Use a Beta(a1, B1) prior for T. Find the posteriordistribution of T given y. Provide the numerical value of a.Round your final answer to 4 decimal places.

Answered: For four pairs of a rare specimen of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The manufacturer of LED lights would like to include as part of their advertising the number of hours an LED is expected to work. A sample of 20 lights revealed the following number of hours worked. 2698 2628 2474 2895 2672 2675 2486 2852 2733 2655 2765 2794 2486 2627 2624 2785 2692 2654 2518 2650 Draw normal probability plot for the above data and make comment. Assuming given data to be approximately normally distributed, Construct 90%, 95% and 99% confidence intervals for the mean number of hours that the LED lights of this brand has worked. Construct 90%, 95% and 99% confidence intervals for the standard deviation of the number of hours that the LED lights of this brand worked.
Let X be the discrete r.v. that represents the number of Boys in a three-child family. Assume that the outcomes boys and girls are equally likely. What is the expected value of this discrete probability distribution? What is the variance?
Obtain the characteristic function of the normal distribution. Deduce the first four central moments.
Once all three lists are generated, add them to create the totals of the 200 trials. Create a discrete random variable relative frequency histogram for this data. Clearly label the axes and scale. Calculate the mean and standard deviation for the roll totals: μ= σ= Use these to define a normal probability distribution for the total on the roll of 3 dice. Compare the probabilities of the experimental discrete probability distribution and the normal curve distribution for several cases listed on the table. Complete the table. Probability Relative Frequency Histogram Normal Curve P(9.5≤x≤10.5) P(x≤3) P(x≥15) P(8≤x≤10) Write a brief paragraph comparing the results of the table above. Discuss any similarities or differences in these results. There are 216 possible outcomes for the roll of three dice. The theoretical probabilities for the outcomes of the roll of three six-sided dice are: Roll Probability 3…
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
Use the three distributions labeled i,ii,iii to answer the following questions (shown in picture upload)
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.4%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho: H = 4.8%; H1: µ ± 4.8%; two-tailed Ho: H = 4.8%; H1: µ > 4.8%; right-tailed Ho: H = 4.8%; H1: µ 4.8%; H1: µ = 4.8%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown o. The Student's t, since we assume that x has a normal distribution with known o. The standard normal, since…
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The manufacturer of LED lights would like to include as part of their advertising the number of hours an LED is expected to work. A sample of 20 lights revealed the following number of hours worked. 2698 2628 2474 2895 2672 2675 2486 2852 2733 2655 2765 2794 2486 2627 2624 2785 2692 2654 2518 2650 Draw a normal probability plot for the above data and make comment. Assuming given data to be approximately normally distributed, Construct 90%, 95%, and 99% confidence intervals for the mean number of hours that the LED lights of this brand have worked. Construct 90%, 95%, and 99% confidence intervals for the standard deviation of the number of hours that the LED lights of this brand worked.
Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.896
A snack company makes packages of grapes and honeydew slices. The weight of an individual package of grapes, G, is approximately Normally distributed with a mean of 3.25 ounces and a standard deviation of 0.91 ounces. The weight of an individual package of honeydew slices, H, is approximately Normally distributed with a mean of 4.51 ounces and a standard deviation of 2.02 ounces. Assume G and H are independent random variables. Let D = G – H. What is the probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices? 0.127 0.230 0.284 0.334

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