2.4-10. A certain type of mint has a label weight of 20.4grams. Suppose that the probability is 0.90 that a mintweighs more than 20.7 grams. Let X equalhe numberOints that weigh more than 20.7 grams in a s le ofcight ts selected at random.(a) How is X distributed if we assume independence?(b) Find (i) P(X = 8). (ii) P(X < 6), and (iii) P(X > 6).%3D

Answered: Image /qna-images/answer/03f6dcf2-f999-41e1-9ff5-6d90656ac563.jpg

Answered: 2.4-10. A certain type of mint has 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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Porphyrin is a pigment in blood and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults x is approximately normally distributed with μ = 38 and σ = 12. What is the probability that x is less than 60?
certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
time, i.e. P(μx-ox ≤ x ≤ μx + 0x). 3. Suppose that people heights are normally distributed with mean of 170 cm and standard deviation of 6 cm. a) What proportion of people are between 165 cm and 175 cm tall? b) Find the minimum ceiling of an airplane such that at most 5% of people walking down the aisle will have to duck. E c) Find the probability that the average height of a random sample of 49 people is greater than 172 cm. 80 F3 4 R % 5 T F6 Y 1 & 7 K ard deviation of the expected U 8 DII
23. Find the cumulant generating function of gamma distribution and obtain various cumulants.
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.

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