The central limit theorem states that the distribution of the mean of independent, identically distributed random variables with finite variance is the normal distribution.

Q: Find the mean and standard deviation  of this random variable.

A: Define the Random Variable, X : Number of tickets bought by a individual Given that, X ~ Discrete…

Q: Show that adding a constant K to a random variable increases the average by K but does not change…

A: Suppose I have  a below data For random variable X 2,5,8,4 consider k= 2 Average of 2,5,8,4 using…

Q: Consider a uniform distribution from 1 to 8.  What is the probability that the random variable has a…

A: From the provided information, Let X be a random variable which follows uniform distribution. X ~U…

Q: What requirements are necessary for a normal probability distribution to be a standard normal…

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Q: what is a gaussian distribution?

A: Gaussian distribution (also known as normal distribution) is a bell-shaped curve, and it is assumed…

Q: The filling machine at a bottling plant is operating correctly when the variance of the fill amount…

A: Solution: Let X be the fill amounts. From the given information, X follows normal distribution with…

Q: The standard normal distribution can be used to calculate probabilities for a normally distributed…

A: Normal dist. has a bell-shaped curve.

Q: The t-distribution is a probability distribution that is used to estimate population parameters when…

A: If we have to estimate the population parameters and the sample size is greater than 30 , we use…

Q: The central limit theorem can be used to analyze round-off error. Suppose that the roundoff error is…

A: The mean and variance of uniform distribution can be obtained as:

Q: If the outcomes of a discrete random variable follow a Poisson distribution, then their: a. median…

A: We know that  if λ is the average number of successes occurring in a given time interval or region…

Q: The mean value of the Poisson probability distribution is numerically equal to its standard…

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Q: In a bell curve distribution, the median is less than the mean and is located to the left of the…

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Q: Calculate the mean (mu)  and variance (sigma squared) of the probability distribution

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Q: A(n) ________________________ distribution has mirror image sides such that if the distribution…

A: Skewness:The degree of symmetry of the distribution is called skewness. There are three measure of…

Q: Can a binomial random variable X have a mean = 7 and the variance 11. Why or why not?

A: Hi! Thank you for the question As per the honour code, We’ll answer the first question since 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: Find the variance of the random variable x ?

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Q: contestant in a baking show has 0.2, 0.7, and 0.1 probability of winning 3, 8, or 10 tickets,…

A: Given that  X 3 8 10 P(x) 0.2 0.7 0.1 Standard deviation =S.D Variance =Var(x)

Q: The expected value of a random variable X that is denoted by u is called its: O a. variance. O b.…

A: The expected value of random variable X that is denoted by mu is called ?

Q: Derive the mean and variance of Bernoulli distribution. Show your complete solutions.

A: Bernoulli distribution is a type of discrete distribution. Based on the bernoulli distribution,…

Q: What is the median of a continuous random variable? What is the median of an exponential…

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Q: assume that the distribution is normally distributed. What is the probability the part is properly…

A: here given mean = 3 standard deviation = 0.08 Y = diameter of Pipe here use standard normal…

Q: Give 1 real life situation where the concept of random variables is applicable and construct its…

A: A random variable is a variable whose values depend on outcomes of a random experiment. It is…

Q: Define Probability Distribution of a Discrete Random Variable?

A: The probability distribution of a discrete random variable is a table that mentions all the possible…

Q: If the outcomes of a discrete random variable follow a Poisson distribution, then their: O A. median…

A: Correct answer is (C) mean equals the variance

Q: Obtain the standard deviation of the random variable.

A: First we have to calculate the E(Y2) to find the variance and then standard deviation. It is given…

Q: What information does the mean (expected value) of a continuous random variable give?

A: Query- What information does the mean (expected value) of a continuous random variable give? Answer-…

Q: Suppose that a random variable z has a standard normal distribution. Use a standard normal table…

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Q: In a parametric statistical test a normal distribution and equal variance is assumed. Select one:…

A: In a parametric statistical test a normal distribution and equal variance is assumed.

Q: The standard deviation of a continuous random variable is its expected value. O True O False

A: Given : The standard deviation of a continuous random variable is its expected value.

Q: The filling machine at a bottling plant is operating correctly when the variance of the fill amount…

A: Probability: If a random experiment results in n mutually exclusive and equally likely outcomes; out…

Q: The central limit theorem states that when sample size isn> 30, then the distribution of sample…

A: CLT: For a r.v having probability distribution either it is known or unknown with population mean μ…

Q: Find the mean of the random variable X.

A: Let X is a continuous random variable. The probability density function is given as,…

Q: The standard normal distribution can be used to calculate probabilities for a normally distributed…

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Q: Determine the mean, variance, and the pgf of the zero-truncated Pois: distribution.

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Q: In a poisson distributed character, the mean number of events is 6. Find the variance.

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Q: One of the characteristics of a standard normal curve is that its variance and standard deviation is…

A: We want to tell you which one is the correct choice

Q: If the random variable X has a general normal distribution with a mean of 3 and a variance of 9.…

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Q: The probability of failing to reject the null hypothesis when it is true is also called the…

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Q: Random samples of a Gaussian distribution will fall within two standard deviations of the mean with…

A: Concept:  68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is…

Q: Determine if the random variables are statistically independent.

A: f(x)=∫yf(x,y) dy        =∫y=02(x2+xy3) dy                     =x2∫02dy +x3∫02y dy            =x2 y02…

Q: The mean value of the Gaussian probability distribution is numerically equal to its variance. True…

A: The Gaussian probability distribution has two parameters mean and variance.

Q: What is the Discrete Variance when sample size is 82 with a probability of 0.82?

A: Formula for variance : Variance = np(1-p)

Q: Random sample of size 4 are drawn from the finite population which consists of the numbers…

A: Solution: x (x-μ) (x-μ)2 2 -4 16 3 -3 9 7 1 1 8 2 4 10 4 16

Q: Derive the mean and the variance of Poisson Distribution

A: The p.m.f. of Poisson distribution is given by P(X=x)=e-m  mxx!        ; x=0,1,2,....…

Q: Which discrete distribution has a difference between their means and variances equal to zero?

A: Here identifying distribution in which mean and variance are equal

Q: Explain how the special formulas for the mean and standard deviation of a binomial or Poisson random…

A: The formula for the mean and standard deviation for binomial or poisson random variable are derived…

Q: Determine whether the value is a discrete random variable, continuous random variable, or not a…

A: here AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS  here we will use definition of random ,…

Q: The probability distribution itself is assumed to be a beta distribution. True or false?

A: Beta Distribution is a probability Distribution, one of its most common uses is to model one's…