Problem Let X and Y be two discrete random variables with the following joint probabilities 2 2 3 16 Find 1) the average information H(X) of the first random variable X; 2) the average information H(Y) of the second random variable Y; 4)

Q: (Sec. 5.2) Let X and Y be the two random variables defined in problem 1. (a) Compute the covariance…

A: Introduction: Suppose X and Y are two discrete random variables with probability density functions…

Q: 2. Let X and Y be independent random variables with means ux, Hy and variances o, ož. Find an…

A: Solution

Q: (TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are…

A: Let X is a random variable. Then the variance of X, denoted by Var(X), is a measure of dispersion of…

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given :   X=0 X=2 X=4 Y=1 0.03 0.02 0.1 Y=3 0.15 0.2 0.1 Y=5 0.2 0.15 0.05

Q: 5) Three uncorrelated random variables X1, X2 and X3 have means X, = 1, X2 = -3 and X3 =+1.5 and…

A: (a) E(Y)= ?  (b) V(Y)= ?

Q: 3. Suppose that X - N(3.2, 6.5), Y ~ N(-2.1, 3.5), and Z ~ N (12.0, 7.5) are independent random…

A: Given  X~N(3.2, 6.5) and Y~ N(-2.1, 3.5) and Z~N(12,7.5)  Note: according to the Bartleby, expert…

Q: 5. Suppose that X and Y are two independent discrete random variables, where X and Y only take…

A: Independent events: Two or more events are said to be independent if occurrence of one does not…

Q: 5. X and Y are two discrete random variables. If the covariance between X and Y is positive, then:…

A:

Q: Question 1: Let X and Y be two discrete random variables with a joint probability distribution given…

A: We have to find given probability.

Q: 2 Two discrete random variables X and Y have 2 P (X = 0, Y= 0) =, = P (X = 0, Y=1) 6. P (X = 1, Y=0)…

A: Given, X/Y 0 1 Totals 0 2/9 1/9 3/9 1  1/9 5/9 6/9 Totals 3/9 6/9 1

Q: 5. Suppose a random variable (X,Y, Z) is equally likely to take any one of the values (1,0, 0), (0,…

A: Given, Points are equally likely hence,   (X, Y, Z) P (x, y, z) (1, 0, 0) 15 (0, 1, 0) 15…

Q: Question 1 1.1 In the single-variable case, we saw that the probability function for a discrete…

A:

Q: 3 4 5 P(X = x) 0.17 0.23 0.44 0.16 i. Show that P X x () = is a probability distribution function of…

A: Given that  Probability distribution of a discrete random variable. x 2 3 4 5 P(x)  0.17 0.23…

Q: 36 1 LetX be a random variable with probability function f(x) x = 1, .. , 3. 49 x2 Calculate the…

A: The expected value of x can be obtained as:

Q: 8. The probability distribution of the discrete random variable X is: \3-x f (x) =(; (4)"()* for x =…

A:

Q: 5. The probability distribution of discrete random variable X is given by k for x = 1, 2, 3 x +1 P(X…

A: In question, Given that X is random variable having pmf P(X =x) = k/(x+1)    x = 1, 2, 3 Then we'll…

Q: Question 2 Suppose Y is a continuous, uniform random variable that can take on any value between O…

A:

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Let X and Y be two discrete random variables with a joint probability distribution.     X=0 X=2…

Q: (2) Let X be a random variable with p.d.f. (k 1<x<10 S(x) = , then (a) k-2 (b) k-8 (c) k- (d) k-3…

A: according to our guidelines we can answer only  first question and rest can be re posted.

Q: 2. (8 marks) Suppose X and Y are independent random variables where X- Exp(1) and Y has a geometric…

A:

Q: Question * Let X and Y be two random variables such that Cov(X,Y) =–3 . Then co(5X+3,-2Y-2)=-20…

A: Given : Let X and Y be two random variables such that Cov(X,Y) = -3.

Q: Question 1: Let X and Y be two discrete random variables with a joint probability distribution given…

A:

Q: If X and Y are independent U (–1, 1) random variables then E (min (X,Y))

A:

Q: Theorem 6.2.6 (Bernoull's theorem) If X, is a binomial random variable with parameters n and p, then…

A: Answer: For the given theorem, Proof:

Q: 3.) Find P (X > Y) where X and Y are independent random variables that satisfy X~ N (2,1) and Y~ N…

A: We have given the following statement.

Q: 2.5.1 The probability function of a random variable Y is given by p(i) = ,i = 0, 1, 2, positive…

A:

Q: Question 6: Let X and Y be two random variables defined on a common probability space (12, r, P). Is…

A: X: Ω →ℝ is measurable. This means X-1B ∈ Γ for all B of Bℝ.  The cumulative distribution function of…

Q: Question Let X and Y be two random variable with E(X) = 1,Var(X) = 2, E(Y) = 2,Var(Y)%3D 2. Then…

A:

Q: 4. The distribution function of the mixed random variable Z is given by for z<-2 z+4 F(z) = for…

A: Answer - Given distribution function of X                  F(z)  =     0            for  z &lt; -2z…

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X = 2 Y…

A: We know that the total probability is always 1.  So,  k+0.15+0.35+0.15+0.2+0.1=1

Q: 1.1 In the single-variable case, we saw that the probability function for a discrete random variable…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

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: Problem 6: Discrete random variables X and Y have the joint PMF x = 1, 2, ..., 10; y = 1,2, . ..,…

A: The joint PMF for X and Y is, P(X,Y)=1100,x=1,2,....,10, y=1,2,......100, otherwise The probability…

Q: 2 Consider two random variables X and Y with joint PMF given. Find P(X < 2, Y < 4). Y = 2 Y = 4 Y =…

A:

Q: 4.22 The random variable x has the discrete probability distribu- tion shown here: -2 -1 2 p(x) .10…

A: We have given that,  Let X be the random variable having discrete probability distribution is,  X…

Q: 17. If a random variable X assumes the values 0 and I with P(X= 0) = 3 P(X = 1), then %3D V(X) is :…

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Q: 3. Three independent random variables X , Y and Z are given with their distribution laws: 2 Y 1 1…

A:

Q: . The cumulative distribution function F of a discrete random variable X is given by Find the…

A: Introduction: If the cumulative distribution function (cdf), F (x) of a discrete random variable, X…

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given Data:   x=0 x=2 x=4 y=1 0.03 0.02 0.1 y=3 0.15 0.2 0.1 y=5 0.20 0.15 0.05

Q: and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and (d) E[XY].

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Q: (i) If X is a random variable and K is a constant, then E(X + K)= E(X) + K

A:

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X = 0…

A: Here, X&gt;0 means X=2 and X=4. And Y≤3 means Y=1 and Y=3.

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X=0 X-2…

A: Given,   X=0 X=2 X=4 Y=1 0.03 0.02 0.1 Y=3 0.15 0.2 0.1 Y=5 0.2 0.15 0.05

Q: Question * Suppose X, Y are two discrete random variables with probability function given by: Y X -1…

A: State whether x and y  are dependent or independent

Q: 13-17. If a random variable X assumes the values 0 and 1 with P(X= 0) = 3 P(X = 1), then nX) is:…

A: Given that, for random variable X,  P(X = 0) = 3P(X = 1) The variance of X ia defined as V(X) =…

Q: Problem 1: A discrete random variable X has possible values x, =f, i 1, 2, 3, 4, 5, which occur with…

A: Given; a discrete random variable X has possible values xi=i2,i=1,2,3,4,5now, probability…

Q: 2.5. Let N be a random variable with distribution function 0 if <0 F(2) = 〈a,2 if 0 < x < 1 Find…

A: Given cumulative ditribution function F(x) as shown belowTo find the P(1/4 &lt; X&lt; 5) According…

Q: 3.Suppose that X and Y are independent random variables for which Var(X)=Var(Y)=3. Find the values…

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Q: 13. Suppose that X and Y are random variables such that Var(X) =9, Var(Y)= 4, and p(X, Y)=-1/6.…

A: We know that, V(X+Y) = V(X) + V(Y) + 2Cov(X,Y)  And V(X-Y+C) = V(X-Y) + V(C) V(C) =0 V(X-Y) = V(X) +…