Let X and Y denote two discrete random variables taking the values in x and y respectively. The collected data over time is represented in the following stochastic model.   Are the X and Y independent? Explain

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Q: Example Let Y. < Ya <.. < Yo denote the arder statistics of a random sample of size n from a…

A: It is an important part of statistics. It is widely used.

Q: Let X be a standard normal random variable and let Y = X². a. Show that X and Y are not independent.…

A: It is given that X be a standard normal random variable. That means, X~N(0, 1) The probability…

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A: Given data :  f(x)=e-x , x&gt;0 0 , otherwise Finding Mean ,…

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Q: Let X₁, X₂ and X3 be mutually independent random variables with Poisson distributions having means…

A: X~Pois(λ) P(X=x)=e-λ λx/x! x=0,1,2,3,..,..

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

A: We have to check whether the probability diatribution is valid or not.  For valid probability…

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Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: The Bernoulli Process Strictly speaking, the Bernoulli process must possess the following…

A: Given that  the Bernoulli process must possess the following properties:   1. The experiment…

Q: Consider the two random variable X and Y. They have the following joint probability mass function: 1…

A: The correlation of X and Y is represented by the coefficient of correlation. For two random…

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Q: Let the random variable X assume the value r, with probability law P(X=r) =q P, Find the moment…

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Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

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Q: Exercise 23. Let X be a random variable having the uniform distribution on the interval (0,0+ 1), 0…

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Q: Let Y be a continuous random variable where 1 ,-3< y< 15 f(y) = {18 0 ,otherwise Then expected value…

A: Let  y be a contineous random variable wherefy=118,-3≤y≤150,     otherwise

Q: Let X and Y be independent Poisson random variables with parameters 0.25 and 0.35,

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X be a random variable with PDF fx(x) = x > 0, %3D DDR

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X1, X2,..., Xn ~ N(μ, 0²) independent random variables. Find the distribution X+X2+…+Xn X= = n…

A: Given Xi~N(μ, σ2) be the iid and i=1,2,...,n  Result: X and Y are independent then E(XY)=E(X)E(Y)…

Q: A +Y. (ii) Let X and Y be independent poisson random variables with respective parameters A and A…

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Q: Let Z and Y be discrete random variables taking values 0 with the corresponding distributionms P(Z =…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

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Q: Let X be a discrete random variable with expectation 1.5 and variance 2. Let Y = -2 X+9. Find the…

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Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

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A: the problem can be solved using the concept of expectation.

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Q: Let X and Y be two discrete random variables with a joint probability distribution given by X = 2 Y…

A: We know that the total probability is always 1.  So,  k+0.15+0.35+0.15+0.2+0.1=1

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A: Given  Yi~exp(1)

Q: fx(x) 4 a -1a

A: We have to find the value of constant for valid pdf.

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A: Introduction: The cumulative distribution function (cdf), of a discrete random variable, X is given…

Q: (a) Suppose rain is falling at an average rate of 30 drops per square inch per minute. What is the…

A: Hello. Since your question has multiple, we will solve first question for you. If you want remaining…

Q: Let Z be a discrete random variable with ?(Z)0. Does it necessarily follow that E(Z^3)=0? If yes,…

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Q: uppose Xn is an IID Gaussian process, with µX[n]=1, and σ2 X[n]=1 Now, another stochastic process Yn…

A: 1.) Xn is an IID Gaussian process. i.e Xn and xn-1 both will follow a normal distribution with µ=1,…

Q: Let X, X, be two independent random variables with Poisson distribution of parameter X=1/2. Then let…

A: We have given that  X1,X2 be two independent random variables  X~Poisson( λ=1/2) Mean=E(x)= λ=1/2…

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given Data:   x=0 x=2 x=4 y=1 0.03 0.02 0.1 y=3 0.15 0.2 0.1 y=5 0.20 0.15 0.05

Q: Y1. Y2. Y, are independent random variables, and .... Y, - Poisson, mean µ,. The fitted values for a…

A: Given the independent random variables Y1, Y2, . . ., Yn and Yi~Poissonμi.

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X = 0…

A: Here, X&gt;0 means X=2 and X=4. And Y≤3 means Y=1 and Y=3.

Q: Let X be a discrete random variable with the following cumulative.distribution function 0. x<0 0.2…

A: Answer:-

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given,   X=0 X=2 X=4 Y=1 0.03 0.02 0.1 Y=3 0.15 0.2 0.1 Y=5 0.2 0.15 0.05

Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

A: We have given that, Let X and Y denote two discrete random variables taking the values in x and y…

Q: (a) What is the probability that X + Y > 1.

A: Exponential distribution is widely used in statistics . It has the unique lack of memory property .

Q: Let X be a discrete random variable with the following cumulative distribution function 0. 0.2 15x<3…

A: Given cumulative distribution function is, F(x)=0, x&lt;00.2, 0≤x&lt;1a, 1≤x&lt;30.6, 3≤x&lt;51, x≥5…

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

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Q: Let X and Y denote two independent Poisson random variables with and .

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: X is an poisson random variable with parameter λ = 4 Calculate P {X ≤ 3}

A: It is given that X is the random variable and the mean given by λ is equal to 4 The probability of X…

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.