If X has a beta distribution with parameters a and B, show that aB V (X) = (a + B)2 (@ + B + 1)'

Q: Consider a random variable X that follows a Beta distribution with E[X] : Find the method of a+1"

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Q: Suppose that a random variable y is uniformly distributed on an interval (0,1) and let c> 0 be…

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Q: 5 Let X1 and X2 be independent and identically distributed random variables that follow an…

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Q: Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a…

A: Here, mean  =50×2 =100 Variance =50×4 =200

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A: 3.3 From the given information, Y denotes the number of bacteria per cubic centimeter in a…

Q: Suppose that X1,..., X, is a random sample from the Normal distribution N(0,0²) with parameter o >…

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Q: If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X…

A: Assuming X is the sample mean of the random samples,consider the following lemma:

Q: A continuous random variable is said to have a Rayleigh distribution with parameter o if its PDF is…

A: Rayleigh distribution: A continuous random variable X is said to follow a Rayleigh distribution with…

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Q: Let X, denote the mean of a random sample of size n from a Gamma(, 1) distribution. Show that Vn (X,…

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Q: para- If the time T to failure of a component follows a Weibull distribution with imeters a and B,…

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Q: Let X1,..., X,|A be iid Poisson(A), and let A ~ Gamma(a, B), with a, B are known. Give two reasons…

A: Given information: The probability density function of the random variable X is as given below:

Q: Suppose X1,..., Xm are iid gamma random variables with parameters 1 and 0 Let X, = E X; ,let W, =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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Q: Develop a random variate generator for a random variable X with the pdf if 0 <x< 1, 2 f(x) = 3 if 1…

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Q: 6. Show that a gamma distribution with a> 1 has a relative maximum at x = (a- 1)B. What happens when…

A: We have to show that : gamma distribution with alpha &gt;1 has a relative maximum at x=(alpha -…

Q: If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value…

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Q: 5. Suppose that X has an exponential distribution with parameter A. Prove that Y = VX has a Weibull…

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Q: Let Y be a random variable with pdf giyen by

A: Given that fy=30y21-y2, 0&lt;y&lt;1 Formula for Ey4 is, Ey4=∫01y4fydy

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Q: If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X > x). P(X > h), then…

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Q: 6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens…

A: Relative maximum =? For a gamma distribution for alpha&gt;1

Q: Let X1, X2, ... , Xn be a random sample with pdf f(x) = (0+1)xº-1, 0sx<1,

A: Given information: f(x)=θ+1xθ-1, 0≤x≤1, 0&lt;θ&lt;∞ Consider, the likelihood function, Lx=∏i=1nfx…

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Q: Find auto-correlation function of a random process whose power spectral density is given by 1+

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Q: Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E(X) = In 2

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A: Given problem is :

Q: Given the random variable x- f(x)=ae for x20. Estimate the moment generating function of x.

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Q: Suppose X1,..., X, are iid gamma random variables with parameters 1 and 0 Let X, = E X; »let Wn log…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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Q: Show that any random variable, X, is uncorrelated with a constant show Cov(X, a) = 0. а.

A: Solution: The given random variable is X and constant is a.

Q: 9. A number of persons are measured for their heights x, weights y and chest expansion z and product…

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Q: 3. Let X1, · ,Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/E÷ Xi and E- X;…

A: Given that X1, . . ., Xn be iid with exponential distribution with mean θ.

Q: The Poisson mass function is given by P(X=x)3e-Mox! for x-0,1,2,3,. and A>0. What is E[X(X-1)] where…

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Q: 2. Show that in a Lorentzian distribution the half width is r.

A: Introduction -   The Lorentizan function is the singly peaked function given by L(x)…

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Q: Let X and Y be two continuous random variables with joint PDF of ху + ) 0<x< 1,0 < y < 2. f(x, y) =…

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Q: 2. It can be shown that if the random variable Trepresents the time to the rth event in a Poisson…

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.