The joint probability mass function of the random variables (X, Y) is given by the followin cable. Please find Var(X +Y) =? Y 1 2 X 1 20 3c 2 3c 2с 3 C 2с 3.

Q: Let Xand Y be two continuous random variables with joint probability density [3x function given by:…

A: Given : E(X) = 3/4  E( X 2)= 3/5 E(Y) = 3/8 E( Y 2)= 1/5 E(XY)= 3/10

Q: Show that the following function is a valid probability mass function of the random variable X.…

A: Sol

Q: Suppose that X and Y are random variables with joint probability mass function 1-1 y-1 22 Px.y(r, v)…

A: a) i) Since P(x,y)≥0        ii) ∑x∑yP(x,y)=2236∑y13y-1∑x14x-1∑x∑yP(x,y)=2236∑y13y-1…

Q: If the independent random variables X and Y have the marginal densities f(x) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 1 2 for 0…

A: From the given information, it is clear that,  fx=12     0<x<20       elsewhereπx=13…

Q: Find μ,μ 2, and σ2 for the random variable X that has the probability density f(x) =⎧⎪⎨⎪⎩x2for 0…

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Q: Suppose that the random variables X and Y have the following joint probability density function.…

A: Given information: The joint probability density function of X and Y is as follows: fx,y=ce-8x-4y…

Q: The random variables X and Y have the joint density: fx,y(x,y) = 2-x-y, for 0<x<1, 0<y<1 0,…

A: Given that :  Joint density function is given. By using this firstly we calculate the marginal…

Q: The joint PDF of two random variables X and Y is given by 6 ху fxy (x,y) = (x² +),0 Y] c) Find Pr[Y…

A: a)Using the formula of…

Q: Suppose that we have 2 random variables X and Y with joint probability density function fxy(x,y) = k…

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Q: The joint probability mass function of X and Y is given by: P (X = 0, Y = 0) = 0.650 P(X = 1, Y = 0)…

A: # joint probability distribution of x ,y is given as then to find varience (x/y=1)??

Q: 3 If X has the density function 2(x+2) f(x)= ,0<x<1 0, elsewhere. Find the variance of the random…

A: Probability Density Function: A continuous function f(x) is said to be the probability density…

Q: X is a discrete random variable having a probability mass function P(X = x) defined as follow X = x…

A: Solution

Q: The probability mass function of a random variable X is as follows: frx) = x! x = 0, 1, 2, ... Given…

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Q: (2) j libäë Q7) A continuous random variable X has the below density function, Find the expected…

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Q: Let Xand Y be two continuous random variables with joint probability density 3x function given by:…

A: We know that, Var(X)= E(X2)-(E(X))2 so from the given values, = (3/5)-(3/4)2 = 3/5 -9/16 =…

Q: The Joint Probolidy density functhon of the randon Voci ables X and y is as Follows ,2 1, ok X<1 A)…

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Q: Determine the constant amount of C so that the random variable X is a valid probability mass…

A: A probability mass function f(x) is said to be valid if ∑f(x) = 1 and f(x) ≥ 0 for all x. Note :…

Q: Two continuous random variables X and Y have the following bivariate probability function which is…

A: The answer is given in the below image.

Q: Find the expected value of the function g(X) = X³ where X is a random variable defined by the…

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Q: (b) Suppose X1, X2, ...,Xn are iid Random variables with density function 1 f(x) = -еxp 20 p(-),…

A: (b)

Q: The random variables X and Y are independent and have probability masses given by: Р(X — 1) — 0.2…

A: Given, the random variables X and Y are independent. P(X=1)=0.2, P(X=2)=0.2, and P(X=3)=0.6.…

Q: Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of…

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Q: Suppose that two continuous random variables X and Y have joint probability density function fay =…

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Q: In the textbook Exercise 5.10, we had to show that 1, 0< yı < 2, 0 < y2 < 1, 2y2 < yı, 0, elsewhere…

A: Just calculate the marginal density at first then calculate expectation and variance.............

Q: Let X and Y be two continuous random variables with joint probability density function given by:…

A: Var(aX)= a2var(X) cov (aX,bY)= a×b×cov(X,Y)

Q: Let X be a random variable with probability mass function  P ( X = 1 ) = 1/2 , P ( X = 2 ) = 1/3 ,…

A: Solution: The given probability mass function of X is

Q: Calculate the mean and variance of the random variable y, whose probability mass function is: f(y) =…

A: Farmula used E(Y)=∑YP(Y=y) Variance=V(Y)=E(Y2)-(E(Y))2

Q: The joint cdf of a random variable X and Y is given by Fxy(x, y) = -e¯ª)(l-e-by) _x≥0, y ≥0, a, b>0…

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Q: The joint probability mass function of X and Y, p(x, y) is given by p(1,1)=p(2,1)= p(3,1)=1/…

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Q: Given the continuous random variables X and Y with joint probability density function: (x, y) = { **…

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Q: Let Xand Y be two continuous random variables with joint probability density (3x function given by:…

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Q: If the probability density of a random variable is given by JK (1 X2), 0< X < 1 0 < X< 1 fx (x) =…

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Q: 2. Consider the following joint probability mass function, fx.y(x, y) of the discrete random…

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Q: The joint probability mass function of X and I, p(x, y) is given by p(1,1)= p(2,1)= p(3,1)= p(3,2)=…

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Q: Let X and Y be two continuous random variables with joint probability density (3x function given by:…

A:

Q: Let X and Y be two continuous random variables with joint probability density (3x function given by:…

A:

Q: Let the joint probability mass function of two discrete random variables X, Y be f (z,y) I= 1,2,3…

A: f(x,y) = xy2/30 x\y y=1 y=2 P(x) x*P(x) x=1   1/30   2/15   1/6  1/6 x=2   1/15   4/15   1/3…

Q: The area of a rectangle is obtained by first measuring the length and width and then multiplying the…

A: Joint pdf  fX,Yx,y=k;where 0.9L&lt;x&lt;1.1L          0.8W&lt;y&lt;1.2W…

Q: Consider two continuous random variables X and Y characterized by the following joint probability…

A: (As per Bartleby guidelines , we can answer only one question . Please upload the other parts…

Q: The probability density function of a continuous random variable Y is given by , -2<ys0 0<ys2 8. (a)…

A: Solution 8a :   (i)  We know that  ∫f(y) dy = 1⇔ k∫-20 (y+2) dy + 2k ∫02 dy = 1⇔k y22 + 2y0-2  +4k…

Q: The joint density function of the random variables X and Y is 6-x-y 0<x<1, 0<y<1-X, 8 f(x, y) = 0,…

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Q: The joint probability mass function of X and Y, p(x, y) is given by p(1,1)=¹ p(2,1)= p(3,1)=…

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Q: Given the continuous random variables X and Y with joint probability density function: f(x,y) = 0Sys…

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Q: The joint pdf of the random variables X and Y is given by cx, x > 0, y > 0, 1 < x + y < 2, f (x, y)…

A: The problem can be solved using concept areal integration.

Q: Let X be a discrete random variable with probability mass function given by 1/4 x = 0 1/2 1/8 1/8 1…

A: For a random variable the probability mass function is function that gives the probability every…

Q: The joint probability function of random variables X and Y is given to be: Зх - у 1<1<4,1<y<2 f(x,…

A: The joint probability function of X, Y is given as f(x,y)= 3x-y9                              1≤x≤4…

Q: If the probability density of a random variable is given by |С ехр(-x/4), 0<x<1 fx (x) otherwise…

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Q: Given the continuous random variables X and Y with joint probability density function: ху x² + 3…

A: Solution

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.