[2]X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.

Q: For the following scores,    X Y 1 7 4 2 1 3 1 6 2 0 0 6…

A: The given data shows the scores of X and Y.

Q: 2. Define the process, t I VY(u)dW(u) + | Vudu Y(t) = What is the variance of Y (t)?

A: Solution Given   Y(t)=∫0tY(u)dW (u)+∫0tuduwe need to find the Y(t)?

Q: A stationary unity mean random process X (t) has the auto correlation function 5. Rxx (T) = 1+…

A:

Q: The lines of regression of y on x and x on y are respectively y = x + 5 and 16r 9y 94. Find the…

A: Answer:

Q: Calculate Karl Pearson's coefficient of skewness from the following data : Profits No. of Cos.…

A:

Q: 5. Let X have the pdf {(x + 1) -1 <x < 1 f(x) = elsewhere. Find the mean and the variance of X.

A: 5. The given pdf is, fx=12x+1       -1&lt;x&lt;10                   elsewhere

Q: Let E(X|Y = y) = 3y and var (X|Y = y) = 2, and let Y have the p. d. f. fv) = {e if y > 0 0 otherwise…

A: Given,  E[X|Y=y] = 3yVar[X|Y=y] = 2 Find var(X) as follows Var(X) = Var(E[X|Y])…

Q: A stationary unity mean random process X (t) has the auto correlation function Rxx (T) = 1+e 21t.…

A:

Q: Let X, and X, be random samples taken from the exponential distributionf (x) = 4e¬4x, 0<x<∞. a) Find…

A: The PDF of the exponential distribution is given by, f(x) = 4e-4x , 0&lt;x&lt;∞ X ~ Exp(4) So, E(X)…

Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: Prove that the mean and variance are obtainable from RX(t)= ln(MX(t)): MEAN=E(X)=Rx'(0),…

A:

Q: Let fix) = 2x, 0 <x<1, zero elsewhere, be the pdf of X. (a) Compute E(X) and Yar(X) (b) Find mean…

A: Expected Value and variance: If X is given as the random variable with the probability density…

Q: Let X have the pdf f(x) = B¬l exp{-x/ß}, 0< x<o∞o. Find the moment generating function, the mean,…

A: The moment generating function is defined as MX(t) = E(etx)

Q: Suppose that X is a continuous unknown all of whose values are between -3 and 3 and whose PDF,…

A: Find the constant c: The value of the constant c is obtained as 1/36 from the calculation given…

Q: X (4) is a WSS process with E [X (t)]=2 and Ryx (T) = 4 + e- 0.1 la, Find the mean 1 and variance of…

A:

Q: (ii) Find the correlation coefficient given the following summations: E(X – X)(Y – Ỹ) = 168, E(X –…

A: To find: Correlation coefficient

Q: Given the auto correlation function for a stationary ergodic process with n. periodic components is…

A:

Q: 20. The lines of regression of y on x and x on y are, respectively, y= x+ 5 and 16x -9y 94. Find the…

A:

Q: Find the mean, variance and the coefficients B1, B2 of the distribution : dF = kx²e* dx = 1,0 < x…

A:

Q: The joint PDF of the random variables X and Y is defined as f(x, y) = 25e: 00 = 0, otherwise (i)…

A:

Q: Suppose that X, and X2 are independent and exponentially distributed random vari- X1 ables, both…

A:

Q: a) Let X1,..., X, be iid with pdf f(x; 0) = 1/0 for 0 0. Find the method of moments estimator of 0,…

A: The method of moments consists in estimating θ by the statistic T(X1, ...., Xn)

Q: If X and Y are correlated variables, then the correlation coefficient between X and Y lies between O…

A: The correlation coefficients for any two variables lies between -1 and +1. So, if the variables X…

Q: Two real-valued RVs, X and Y, have joint PDF 1 p(x, x2) = exp 2TV1-r (x; – 2rx,x2 2(1 - r) where -1…

A:

Q: 2y Q1. If f (y) = for 0 < y<k for what value of k does Var(Y)=2? Q2. Let f (y) = 3(1 – y)² for 0 < y…

A:

Q: Q1) Test a correlation relationship by using Pearson Superman coefficients. 2 2 2 1 1 1 y 3 X 4 2 2…

A:

Q: Find the correlation co-efficient between X and Y, which are jointly normally distributed with 1 1…

A:

Q: (b) Suppose that X has moment generating function Mx(t) = ( et +) (i) Find the p.m.f. of X. (ii)Find…

A:

Q: 1. Let X be an RV with PDF - f(x) = {1 = |x| a. Find the mean of g(x) = 5x² - 1. b. Find the…

A:

Q: iv) Explain why, in this instance, the correlation of X and Y,p(X,Y), is equal to the covariance of…

A:

Q: The coefficient of correlation between X and Y is - and o = a, of = 4a, and %3D %3D ož = 114 where Z…

A: Given: Z=3X-4Y. The coefficient of correlation between X and Y is 13and σx2=a, σy2=4a,σz2=114

Q: Let X1 and X2 have the joint pdf f(x1,x2) = x1+x2, 0 < x1 <1 and 0< x2< 1. Find the conditional mean…

A: It is given in the question that X1 and X2 are two random variables having joint probability density…

Q: For the following function, find the constant c so that f(x) is a PDF of a random variable X. 2- 2…

A:

Q: Q2: Suppose that the j.p.d.f.,ƒ (x, y) = {(x² + y), 0<x< 1, 0 <y<1 zero elsewhere. Find: a- The…

A:

Q: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given:  X + 3Y + Z + 6

Q: Let E(X|Y = y) = 3y and var(X|Y = y) = 2, and let Y have the p. d. f. %3D %3D if y > 0 e-y fG) = lo…

A: Given EXY=y=3y      and   varXY=y=2 Y have the p.d.f       fy=e-y        if   y&gt;0 0…

Q: 1. Find the average value of the function f(x) = x³ + 3x + 5 on [0,2].

A: The given function is

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

A:

Q: - Given the auto correlation function for a stationary ergodic process with no 4. periodic…

A:

Q: Let X1, X2 be a random sample of size n : = 2 from the exponential ity function (pdf with an unknown…

A: Given information: Given that the random sample X1, X2, … ,Xn is from an exponential distribution…

Q: 4. (1) The density function of X is (2x, f(x) = 0, (a) Find the mean E(3X+1); (b) Find the variance…

A:

Q: For the following function, find the constant c so that f(x) is a PDF of a random variable X. 2- for…

A: The random variables are of 2 types, discrete and continuous. Probability density function to…

Q: hat Xt = 1+ Z + 0(ZŁ-1+ Zt-2+ • · · +) %3D hite noise with mean zero and variance one. ationary for…

A: *Answer:

Q: Q3/A/ Let X be a r.v with p.d.f f(x) = e-ll - co <x<0, then the value of variance of X is -

A: Given : X is a random variable with PDF             fx=12e-x , -∞&lt;x&lt;∞ To find : Variance of X

Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

A:

Q: Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The…

A:

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,

Q: 2.7 For an exponential distribution fx(x; p) = {ue *; (iz %3D e. w. where u

A: Given density function, This is the exponential distribution with parameter μ. a) Mean: b)…

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.