Assume that Y_n=X+W_n, where X is standard Gaussian random variable N(0,1) and W_n is white noise WN(0,4). Let the prediction formula is W_0*=aY_0. The value of a is A 0 B 4/5 1 D 4

Q: If the random variable X follows N (0, 2) and Y = 3X, find the mean and vari- %3D ance of Y.

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Q: Suppose X is a random variable such that EX = 50 and V arX = 12. Find (a) E(X 2 ) (b) E(3X + 2) (c)…

A: The given X is a random variable with EX=50 and VarX=12.

Q: 3. Travelers who have no intention of showing up often fail to cancel their hotel reservations in a…

A: The following data has been given: 18,16,16,16,14,18,16,18,14,19 The sample size is n=10.

Q: Let X be a random variable with only two possible values: (1,-1}. Then the set of possible values of…

A: Given Let X be a random variable with only two possible values: (1,-1). Then the set of possible…

Q: S Suppose that the time (in hours) required to repair a machine is an exponentially distributed…

A: The distribution of the repairing time for the machine is specified to be distributed exponentially…

Q: coin with two sides - H and T,  6 times. Suppose the probability of getting a heads is 1/3.   Let…

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

Q: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: 3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r

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Q: (2x-x*), 2x-x²), 0<xs2 Suppose X is random variable whose p.d.f. is f(x)={4 0, elsewhere Find the…

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

Q: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Var(aX) = 16 Var(bY) = 36…

A: Suppose we have two random variables X and Y. For a, b &gt; 0, a2+b2=13. Here we use the…

Q: Show that their correlation coefficient is p =1_if a > 0 for any b =- 1 if a<0 for any

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Q: 3 The random variable X ~ B(40, 0.4). Find: a P(X 16) e P(11< X< 15) d P(10< X< 17)

A: The mean is computed as: The standard deviation is computed as In the given case, the required…

Q: For a uniform random variable U∼U(2,11)U∼U(2,11), find the probability P(U<9)P(U<9): P(U<9)=P(U<9)=…

A: GivenA random variable x~Uniform(2,11)f(x)=1b-a      ; a&lt;x&lt;bf(x)=111-2f(x)=19  ;…

Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: We want to find V(aX+bY)= ?

Q: Suppose X1, X2, X3 are m generating functions, Mx, (t) = e²²², Mx, (t) = e²t + 3t², and Mx, (t) = (²…

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Q: Exercise 8. Suppose X1, X2, , Xn are independent random variables with X; ~ N(Hi, o), 1<i<n. If X =…

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Q: The number of times that a person has a cold each year is a Poisson random variable with parameter λ…

A: Define the event E as the drug works, thus P(E)= 0.75 The drug that doesn't work is the complement…

Q: The probabilities of a random variable X are given as when x, =, Plz) =} 1 2 -1 1 P(x,) = 2 and X2…

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Q: When X is a binomial random variable, then the probability X ≤ r successes can be found using the…

A: Given  X is a binomial random variable Number of trials=n=167 Probability of success=p=0.051

Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

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Q: let X be a random variable and X-B(10, 0.81) find P(x=7)

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Q: When X is a binomial random variable, then the probability X ≤ r successes can be found using the…

A: Given  X is a binomial random variable n=No. of trials=125 p=Probability of success=0.016

Q: A discrete random variable X can take 3 outcomes: 0,1 and 2 with probabilityP(X = k) = c(k + 1)2, k…

A: It is known that the random variable X takes 3 outcomes: 0,1, and 2 with the corresponding…

Q: Suppose that X is a N(3,4) random variable and suppose that Y=2X-1. Determine P(Y>8).

A: We have, Let X be the random variable from normal distribution i.e,  N(3, 4) and Y = 2X-1 Then,  We…

Q: A coin is tossed 3 times and then a die is rolled. Let X be the number of heads times the number of…

A: Given that A coin is tossed 3 times and then a die is rolled. Let X be the number of heads times the…

Q: If a dicrete random variable x takes only three values 2,5 and 9 and that p(x=2)= 0.2 , p(x=5) =…

A: We have to find p value..

Q: If Xn, n > 1, independent random variables and Xn 4 X (a random variable X), are

A: A degenerate distribution (sometimes called a constant distribution) is a distribution of a…

Q: At the 5% significance level, does it appear that price of bus trips per week, population or average…

A: Solution: Given information: k= 4 independent variables  n= 26 observation.

Q: If the random variable X is distributed through the N ( 20 , 25 ) then P ( X > 30 ) =

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Q: Question * Suppose that X and Y are random variables with E(X) = 2. E(Y) = 5 and E(X²) = 8, E(Y) =…

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Q: The joint PMF of two random variables X and Y is given by (k(2x + y), ((2x) Pxy (x, y) 0, Where k is…

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Q: If X and Y are independent random variables with X~N(2,32) and Y~N(1,42), find P(X<Y). (You need to…

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Q: Where does the z=2 come from? Just from X, and Y also being random variables?

A: Solution of the asked question is in step below.

Q: Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X − Y) = 2,…

A: SOLUTION: Cov(X,Y)=np(1-p)-1

Q: X given Y.   Y=0 Y=1 Y=2 Y=3 Y=4 X=0           X=1           X=2

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Q: 3. A) If X and Y are independent random variables with variances o variance of the random variable Z…

A: In question (a) X &amp; Y are independent Variance of x =5 ,  Variance of Y=3 Z= - 2X + 4Y - 3 We…

Q: Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).

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Q: Prove that the variance of a beta-distributed random variable with parameters a and 3 is αβ (a + B)²…

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