A health food store currently has 100 pounds of almonds in stock, which it sells to customers in 2-lbbatches. Let X be the number of batches purchased by a randomly chosen customer. Suppose X as pmfxp(x)0 1 2 30.2 0.4 0.30.1(a) Compute E(X) and V(X).(b) Compute the expected number of pounds left after the next customer has made their purchase and the variance of thenumber of pounds left. [Hint: The number of pounds left is a linear function of X.]

The information provided in the question are as follows : Let a random variable X be the number of…

Answered: A health food store currently has 100…

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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The inhabitants of a city develop skin cancer at an approximate rate A. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: n ~ Poisson(X) X\n - Binomial(n, p) Question 5: What is the distribution of n X? n – X|X ~ Binomial X(1-p) 1- p We do not have enough information to answer this question. n|X Poisson(Xp) On - X|X ~ Poisson(A(1 – p) 1 for n > x n|X ~ fn|x (n|x) = n! 1- Di-o i! 0.w.
Consider the Keynesian consumption function Yt = B₁ + B₂x2t + &t where yt is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0
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A random variable X has a p.d.f. f(x) given by (k(x+2) 0 < x < 3 f(x)= otherwise a. Find the constant k. b. Find the cumulative distribution function of X.
How would you write down a linear univariate model in which turnover, T, depends on assets, K, and an error term, u? Select one: log T = a + bxK+u T= a + bxK+u log K = a + b x log T + u T= a + b/K+u log T = log a + u
1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.
The inhabitants of a city develop skin cancer at an approximate rate X. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: ~ U Poisson(A) X\n - Binomial(n, p) Question 4: What is the marginal distribution of X? Hint: two primary ways to do this: 1. you can summate out n from the joint distribution directly (more straightforward, but tricky algebra) o Pay attention to the lower limit of n o Remember that i=0 2. use MGFS + iterated expectation: E[etx] = En|Exn[etx n|| and then recognize the distribution corresponding to the MGF (need to understand MGFS and iterated expectation). o Obtain the inner expectation by using the Binomial theorem. O X Binoтial(n, Ap)…
Customers arrive at a facility according to a Poisson process N(t) of rate λ = 4.5 customers/hour. Each customer is admitted to the facility with probability p = 0.8. All customers, who are not admitted, leave and do not come back. Let X(t) be the number of customers admitted from time 0 to time t. Compute the following: (a) The mean value E[X(6.5)] = 23.4 (b) The probability P(X(6.5) = 23) = = (c) The conditional probability P(X(6.5) = 23 | N(6.5) = 30) = %. %. Note: For parts (b) and (c), enter your answers as percentages but do not type the percent sign.
A problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.

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