3. Coin with random bias. You are given a coin but are not told what its bias (probability of heads) is. You are toldinstead that the bias is the outcome of a random variable P~ U[0, 1]. To get more infromation about the coinBinom(10, P).bias, you flip it independently 10 times. Let X be the number of heads you get. Thus XAssuming that X = 9, find and sketch the a posteriori probability of P, i.e., fpx (p|9).

Answered: Coin with random bias. You are given a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 16 18 15 12 14 17 17 11 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: μ = 14; H1: μ > 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume…
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A poll of n voters is to be taken in an attempt to predict the outcome of a by-election in a certain riding. Specifically, you are interested in the proportion of voters that will vote for a certain candidate, Candidate A n = 430 voters have been randomly chosen, each has indicated what candidate they will vote for. You are to count the number, out of 430, who say they will vote for Candidate A. This count is measured by the random variable X. You find X = 169. (a) Find a 94% confidence interval for p, the proportion of all voters who will vote for Candidate A. Use at least four decimal points for your lower and upper bounds. Lower Bound - Upper Bound= (b) Interpret the meaning of the interval you found in part (a). The proportion of ? ✓that will vote for Candidate A is ? > % and %. (Enter your answer to at least two decimals.)
Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)
Mike has a deck of standard poker cards with some cards missing. He wants to estimate the probability, p, of drawing a spade. Every day he makes an experiment. At the end of each experiment, he records the maximum likelihood estimator of the probability of observing a spade and places the drawn card back and shuffles the deck. Let X; be a random variable, taking value 1 if the i-th card draw of an experiment results in an even number and 0 if it results in an odd number. Clearly, X, ~ Bernoulli(p). Recall the MLE of a Bernoulli is p MLE The following are the outcomes of 5 experiments, one of which involved 8 card draws, two of which involved 6 card draws and two of which involved 4 card draws. Which experiments lead to the same MLE of p? Select all that apply. O (1 = 0, x2 = 1, r3 = 0, x4 = 0, r; 1, 6 = 0, x7 = 1, Is = 1, xg = 0, r10 = 1, 111 = 0, 112 = 0) O (1 = 1, a2 = 0, r3 = 1, x4 = 1) O ( = 0, x2 = 0, r3 = 0, r4 = 0) O (21 = 0, x2 = 1, £3 = 0, T4 = 0, x5 = 0, x6 = 0, r7 = 1, rg 0)…
You are to wait at a bus stop for the bus to arrive. The bus arrives every 30 minutes, but you do not know the exact time (in minutes) it will take to arrive. Thus, you can wait any time (continuous) between 0 and 30 minutes, and you believe all wait times are equally likely. Let X be the random variable of the amount of time in minutes you will wait for the bus. a. What distribution can be used for the random variable X? b. What is the probability that you wait exactly 5 minutes? What is the probability that you wait exactly 5 or 10 minutes? c. What is the probability that you wait more than 20 minutes?

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