1. The random variable Y = X² does not have a normal distribution because the 1 2 e 1 probability density function of Y is y 202 True False 2. The random variable Y = aX + b, a and b nonzero constants have a normal distribution 1 because the probability density function of Y is 2g2 True False

Q: Assume that X and Y are two random independent random variables with mean 2 and 3 and variance 2 and…

A:

Q: Calculate the correlation between Corr(exY, ex)

A: Given: Corr(exy,ex)

Q: A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y.…

A:

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: 7. Calculate the variance of g (X) = 2X + 3, where X is a random variable with probability…

A: The given data is as follows: x0123f(x)

Q: Let the random variable Y = a + bX. Then, µy = bux. O True O False

A: Given statement isY=a+bX

Q: Let (X,Y) be a bivariate normal random variable. Assume that the covariance between X and Y is 0.…

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

Q: Question B) If the joint pdf of the continuous random variables X and Y is: fxy(x, y) = XY for 0<x<2…

A:

Q: Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4)…

A: X1 and X2 are two independent normal variates  mean and variance (0,1) and (0,4) respectively. Then,…

Q: Let X be a random variable with probability function f(x) = 36 1 49 x² Calculate the variance of X.…

A: f(x)=

Q: we are evaluating two random variables X and Y with probabilitydistribution equal to: p(x, y) = P (X…

A:

Q: X and Y are two discrete random variables, the following table summarizes their joint probability…

A: For a :  P(Y=1)=P(Y=1∩X=0)+P(Y=1∩X=1)0.216=a+0.096a=0.120 For b :…

Q: Be quick please

A: The joint probability distribution of X &amp; Y is given as:     X 0 1 2 Y 1 0.1 0.2 0.1 2…

Q: 1. The random variable Y = X2 does not have a normal distribution because the probability density…

A: Given that,  X~ N(u,σ2)  Where u is mean and σ2 is variance of X.  P.d.f. of X is given by,    Y= X2

Q: te random variable. Let E(X)=10 and Var(X)=5. Since Y = x2 + 3X, What is E(Y)=?

A:

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

A:

Q: 4. Determine the values of c so that the following functions represent joint probability…

A: f(x,y)=c  ,  for x=-2,0,2  ; y=-2 , 3

Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: Let X be a random variable with mean 6 and variance 3. Let Y be the random variable counting the…

A: Given that  E(X) = 6 , V(X) = 3 Let Y be the random variablecounting the number of times the number…

Q: Three zero mean, unit variance random variables X, Y, and 2 are added to form a new random variable,…

A: Random variables and  have zero mean and unit variances.That is:  and These variables are added to a…

Q: 7- Let X be a random variable with probability density function x=1,2,5 f(x)=8 O.w. (a) Find the…

A: Result used  Y=ax+b  E(Y)=aE(X)+b  V(Y)=a2V(X)  Var(X)=E(X2)-(E(X))2

Q: 1. The random variable Y = X2 does not have a normal distribution because the probability density…

A: The p.d.f of normal distribution is given by,

Q: Q1. The density function of the random variable X is given by f(x) =% %3D 2. a) Verify that the…

A:

Q: 1. Explain how to generate a random variable X distributed as the Cauchy distribution, whose…

A:

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

A:

Q: 5. Suppose that X is a discrete random variable with probability density function х%3D1, 2, 3, 4.…

A: In question, We have given the pdf of X which is f(x). Then we'll find the value of E(X). The…

Q: Assume that a joint probability distribution function is given by: p(x,y) X 0 5 10 Find: •E(x), E…

A: The joint probability distribution function is given by, P(x,y) y 0 5 10 15 x 0 0 0.1 0 0.1…

Q: Let ξ and η be independent standard normal random variables. Find the distribution of X = ξ/η

A:

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

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: Let Z be the standard normal random variable. Let X1 = Z, X2 = -Z be independent random variables.…

A: We have given that,  Z from the standard normal distribution with mean = 0 and variance = 1 i.e,…

Q: Pr(Y) 0.5 We know X and Y are independent, so Pr(XIY) = Pr(X) and vice versa, Pr(YIX) = Pr(Y) for…

A: The formula for correlation for X and Y is, CorX,Y=CovX,YVarXVarY Then the formula for covariance…

Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: Two Gaussian random variables X and Y have variances o =9 and o = 4 respectively, It is known that a…

A:

Q: 2) Consider the random variable Y has a normal distribution with the following probability density…

A: Given Y follow normal distribution and its probability density function is shown below…

Q: 5. Suppose that X is a discrete random variable with probability density function x = 1, 2, 3, 4.…

A: Given: p(x)=cx2