How are different chi-square distributions identified?

Q: Derive mean and variance of gamma distribution.

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Q: Find mode of Poisson distribution.

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Q: Discuss a continuous uniform or Rectangular distribution and its properties and show its…

A: A uniform distribution is a type of probability distribution in which all the outcomes are equally…

Q: What are Normal Distributions?

A: The normal distribution is often called the bell curve because the graph of its probability density…

Q: Write down the important properties of the Normal Curve.

A: A normal curve is identified using the values of the mean and standard deviation to show the…

Q: In the normal curve, the measure of variability all coincides at the center. O TRUE FALSE

A: True or False

Q: The number of small air bubbles per 3 feet by 3 feet plastic sheet has a Poisson distribution with a…

A: The plastic sheet has a poisson distribution with a mean number of 2.3 per sheet; λ=2.3

Q: What are the relationships, if any, between uniform, humped, skewed, and kurtosis distributions? Are…

A: uniform distribution a uniform distribution, also known as rectangular distribution is defined as a…

Q: Why do t distributions tend to be flatter and more spread out than the normal distribution is?

A: Formula for t score; Formula for z score; Here s shows the sample standard deviation,  shows the…

Q: To calculate normal distributions values must be?

A: Standard normal distribution: The standard normal distribution is a special case of normal…

Q: A manufacturer makes screws with a mean diameter of 0.15 cm (centimeters) and a range of 0.10 cm to…

A: Here Given  the screw diameter s range is 0.1 to 0.2 cm .

Q: How do you distinguish among the infinitely many different chisquare distributions and their…

A: As the degrees of freedom of the chi-square distribution increases, the distribution becomes nearly…

Q: Areas under the normal curve are positive values. True or False

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Q: The top 10% of a normal distribution is above what z-score?

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Q: Find the value of x for 16 degrees of freedom and an area of 0.025 in the right tail of the…

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Q: The number of traffic accidents per week in a small city has a Poisson distribution with mean equal…

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Q: What are Exponential and Erlang Distributions?

A: The sum of n of exponential (β) random variables is a gamma(n, β) random variable. If the…

Q: A random variable that can be used of the gamma distribution is

A: Random variable can be α=4,β Mean and variance can be, E(X)=αβ=4βVar(X)=αβ2=4β2 Size of sample is…

Q: it be appropriate to use a normal distribution to approxi- mate the binomial distribution?

A: for normal distribution to approxiamte  the binomial distribution  np ≥10  and n(1-p)≥10

Q: Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed…

A: Given that  Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly…

Q: Sketch the normal distributions with μ = 6, σ = 4

A: The mean is 6 and the standard deviation is 4.

Q: Find the percentile points under the normal curve of each of the following then show their graphical…

A: (1) Obtain the value of 37th percentile. The value of 37th percentile is obtained below as…

Q: Why is the standard normal curve sometimes referred to as the z-curve?

A: In this case, we need to explain the reason for the standard normal curve, which is sometimes…

Q: Can we find the area of the standard normal distribution using calculators only? If yes, How?

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Q: Burger Hut sells 224 burgers on an average day, with a variance of 9 burgers. How many burgers…

A: Given: Population average number of burgers sold μ=224 Population variance σ2=9 Here, the number of…

Q: If a sample is randomly collected, we can be assured that the data follows a normal distribution.…

A: We know that ;  Any randomly collected data follows normal distribution if and only if data set must…

Q: Calculate the mean and variance of this distribution using the MGF obtained in (a).

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Q: Write out the content of central limit theorem (CLT). Then use CLT to discuss the relationship of…

A: The Central Limit Theorem states that for any distribution, even very skewed or non-uniform ones, if…

Q: What is the area under each curve of chi-Square distribution? Explain.

A: The distribution of the chi-square statistic is called the chi-square distribution. The chi-square…

Q: Define Concept of Distribution of β^1 with Normal Errors?

A: Introduction: The multiple linear regression equation of the response variable, y, on k predictor…

Q: Describe Normal and Chi-Square Distributions?

A: There are different types of distributions. The basic distribution with probability of success for…

Q: The following table shows the distribution of uric acid determinations taken on 250 patients. Do…

A: Given data, Uric Acid Determination Observed Frequency Midpoint 0-0.99 1 0.495 1-1.99 5 1.495…

Q: a. Reflect how normal distribution will be useful in your field? Give an application related to…

A: Normal distribution is one of the very important tools used in statistics. It helps to determine…

Q: The hypergeometric distribution is used for situations when sample observations are replaced in the…

A: False

Q: What is the difference between Gamma distribution and Chi-Squared Distribution

A: What is the difference between Gamma distribution and Chi-Squared Distribution

Q: What is normal distribution?

A: The normal distribution: A continuous random variable X is said to follow normal distribution with…

Q: How do you identify different chi-square distributions?

A: The chi-square distribution curve varies as the degrees of freedom vary.

Q: The F distribution with 4 degrees of freedom is given by: Image 1 If you take random samples of…

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Q: 2. The amount of sunscreen applied by women aged 21 to 30 years follows a bell-shaped distribution…

A: Given;  x be the amount of sunscreen applied follow normal distribution with mean mu=0.6 and…

Q: Derive mean of gamma distribution.

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Q: What are the two frequencies measured during the Chi-Square Goodness of Fit test and what is the…

A: The test statistic for chi-square goodness of fit is,

Q: The length of time a part lasts after continuous usage follows a Weibull distribution (in hours)…

A: Assume, X be the random variable representing the length of time a part lasts (in hours), which…

Q: The data for a chi-square test consist of numerical scores non-numerical categories ranks…

A: The data for a chi-square test consist of frequencies. It is commonly used for testing relationships…

Q: show how to derive the formulas of mean and variance of a normal distribution (parametric families…

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Q: Why do we need to convert normal distributions to standard normal distributions? Please explain in…

A: Q : Why do we need to convert normal distributions to standard normal distributions

Q: What is the difference between symmetric and standard symmetric distributions?

A: symmetric and standard symmetric distributions

Q: When taking a sample for research we need to be mindful of the Central Limit Theorem which assumes…

A: Central limit theorem :  The central limit theorem tells , exactly what the shape of the…

Q: Define negative binomial distribution.

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Q: What is the correct expression of the integral of the probability function of a normal distribution…

A: The Normal Distribution : 1. The normal distribution is symmetric with scores more concentrated in…