The profit for a new product is given by Z = 3X-Y -5. X and Y are independent random variables with Var(X) = 1 and Var(Y) =2 what is the variance of Z?

Q: The demand for a commodity is given by Q = β0 + β1P + u, whereQ denotes quantity, P denotes price,…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: The discrete random variable X has probability mass function kx x 2,3 x+1' 2kx P(X =x) = x=4,5 x-1'…

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Q: If the random variable X and Y have the joint probability distribution f(x, y) = x+y, 0<x< 1,0 <y<1…

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Q: Let (X, Y) be BVN(0,0, 1, 1, p). Find the variance of XY.

A: Given that; (X, Y)~BVN(0, 0, 1, 1, ρ)⇒X~Normal(0,1) and Y~Normal(0,1)Y|X=x~Normal(ρx, 1-ρ2) We know;…

Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

Q: Find the variance with solution

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Q: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 find the mean and variance of…

A: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 We need to find the mean and…

Q: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…

Q: Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over…

A: Given, The data set is: X Y 1 0 0 1 -1 0 0 -1     To find, The correlation coefficient…

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. .…

A: X follows a  normal distribution with , µ= -1 , σ= 1. Y follows a  normal distribution with , µ= 1 ,…

Q: If X and Y are independent random variables with variances σ2 X = 5 and σ2 Y = 3, find the variance…

A: Given:VX=5 and VY=3

Q: For an initial investment of 100, an investment yields returns of Xi  at the end of period i for…

A: Given that, the initial investment is 100 and the investment yield is X1 and X2 at the end of period…

Q: If X-N(0, 1), then Y = 2X + 1 is distributed: Normal with mean 1 and variance 0 O Normal with mean 3…

A: Given that  X~ Normal( Mean = 0 , Variance = 1 )

Q: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: first model: y = 0.48y, +ê- 0.41 %3D -1 where variance is 0.85 and SSR= 680. Second model: y. 0.4…

A: Given two models yt=0.48yt-1+ε^t-0.41ε^t-1 where variance is 0.85 and SSR=680…

Q: What value of C minimized B(X – C), where X is a random variable?

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Q: Use this covariance matrix to find the estimated variance of the estimated mean of y when z = 8.…

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Q: Two independent variables x, and x, are with means 5 and 10 and variances 4 and 9. If u = 3x, +4x,…

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Q: Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected…

A: Given: A list of n stocks Stock i has expected revenue rate μi with variance σi2 for i=1,2,...,n…

Q: he variance of the event of a coin being thrown four times equal to the center of gravity is the…

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Q: Find a such that aY is an unbiased statistic for 0 and find its variance. (Note that the roles of X…

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Q: The following table gives the total endothermic reactions involving sodium bicarbonate   Final…

A: Note:Hi! Thank you for posting the question. However, from the given data, the problem was not…

Q: X and Y are independent. If we are given P(X = 0) = P(X =1) = P(X =2) = }, P(Y = 1) = 3. P(Y = 2) =…

A: The question is simple and formula based, we need to know the mathematical formulas which are used…

Q: If x and y are two independent random variables, show that +y:x-y={:+}-{:*+), where r+y:x-y denotes…

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Q: Suppose W = (aX + 3Y) 2 where Y, X are two random variables with zero mean and variances 20x = 4,…

A: As, X~N(0,4) and Y~N(0,16) E[x] = 0 Var[x] = 4 E(x)2 - [E(x)]2 = 4 E(x)2 - 0 = 4 E(x)2 = 4 Now, E[y]…

Q: Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter e >…

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Q: dataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are…

A: This problem is based on the sample variance and data sets.   To show -  If sample variance is zero…

Q: The expected value of the transformation is 0 and the variance is 1. So if Z=0.2, when u = 3 and o =…

A: The value of Z is 0.2, mean is 3, and standard deviation is 0.2.

Q: The distribution of z-scores corresponding with a population of scores always has a variance of…

A: The distribution of z scores follows standard normal distribution.

Q: X and Y are random variables that are the same normally distributed variables as in the previous…

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Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x =0 (ii) 1Sx<4 eor…

A: GivenThe variance of a poisson variate is 3in poisson distribution the parameter of mean and…

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: The lines of regression of y on x and x on y are, respectively, y = x + 5 and 16x - 9y = 94. %3D…

A: Solution is given:

Q: Compute the residual

A: here given regression line y = 24+5x   residual = actual value - predicted value

Q: 17. X and Y are independent random variables with means 10 and 20 and variances 2 and 3 respectively…

A: We have given that  X and Y are independent random variable.  Mean (X)=10 , Mean (Y)=20 And Var(X)=2…

Q: Find out the regression coefficients of Y on X and X on Y from the following data: ΣΧ= 50, X= 5 , Σ…

A: It is given that variance of X is 4 and the variance of Y is 9.

Q: 4) Find the variance V(X).

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Q: Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y…

A: Given that, V(X)= V(Y)= 1 So  V(Z) = V(X+bY)  = V(X)+b2V(Y)  { x and Y are independent} = 1+ b2

Q: Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4

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Q: Suppose that the response y is generated by y = f(x) + €, where is a zero-mean Gaussian noise with…

A: Given Information: Consider the response y which is generated by:     y=fx+ε Where ε is a zero mean…

Q: For least-squares to work well, we need: the relationship between x and y to be non-linear.…

A: We have given the following statement about the least square.

Q: There are two random variables X and Y, and their correlation coefficient pX,Y = 0.7. Now, we have…

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Q: Q1. If Var(X)=3, what is Var(2X + 1)? Q2. Compute the variance for a uniform random variable with a…

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Q: The mean of the random variable X is ux = 38 and the coefficient of variation is Vx=0.37. Let Z be…

A: Z = x - μσ

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!