Let X ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2...

Let X ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2 fX(2) = 1 2 fY (3) = 1 3 fY (4) = 2 3 Answer the following questions (a) Write down the joint PMF

(b) Calculate P(X + Y 6 5) and P(Y −X > 2)

(c) Calculate E(XY ), E(X2Y ), E(︁X2+1 Y−2)︁

(d) Calculate the Cov(X,Y ), Cov(1−X,3Y + 2) and Var(2X −Y ) (

e*) Calculate Cov(XY,X), Cov(XY,X + Y ) and Var(︀X Y)︀

Expert Solution

milcah answered 1 year ago

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s: ?x(1)= 1/2 ?x(2)= 1/2 ?Y(3)= 1/3 ?Y(4)= 2/3 (a) Write down the joint PMF (b) Calculate ?(? + ? ≤ 5) and ? (? − ? ≥ 2) (c) Calculate ?(?? ), ?(?2? ),Calculate E((X2+1)/(Y-2)) (d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? ) (e) Calculate C??(??, ?), C??(??, ? + ? ) and V?? (?/Y)

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s: ??(1)= 1/2 ??(2)= 1/2 ??(3)= 1/3 ??(4)= 2/3 Answer the following questions (a) Write down the joint PMF (b) Calculate?(?+?≤5)and?(? −?≥2) 2 ?2+1 (c) Calculate ?(?? ), ?(? ? ), E ? −2 (d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? ) (?*) Calculate C??(??, ?), C??(??, ? + ? ) and V?? ?

Let X and Y be independent geometric random variables with parameter p. Find the pmf of...

Let X and Y be independent geometric random variables with parameter p. Find the pmf of X + Y

Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2,...

Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2, 4]). a) FindP(X<Y). b) FindP(X<Y|Y>3) c) FindP(√Y<X<Y).

. Let X and Y be a random variables with the joint probability density function fX,Y...

. Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { 1, 0 < x, y < 1 0, otherwise } . a. Let W = max(X, Y ) Compute the probability density function of W. b. Let U = min(X, Y ) Compute the probability density function of U. c. Compute the probability density function of X + Y ..

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

Let X and Y be independent Poisson random variables with parameters 1 and 2, respectively, compute...

Let X and Y be independent Poisson random variables with parameters 1 and 2, respectively, compute P(X=1 and Y=2) P(X+Y>=2) Find Poisson approximations to the probabilities of the following events in 500 independent trails with probabilities 0.02 of success on each trial. 1 success 2 or fewer success.

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y is a uniform (0,6). Let W=2X-Y and Z= 2X+Y. a) Find the expected value of X, the expected value of Y, the variance of X and the variance of Y. b) Find the expected value of W. c) Find the variance of W. d) Find the covariance of Z and W. d) Find the covariance of Z and W.

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and...

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and y=1,2 calculate the covariance of x and y calculate the correlation coefficient of x and y Thank you

Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z...

Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z := X + Y ? (b) Find the pdf of Z. (c) Find MZ(t). (d) Let U = e Y . What is the range of U? (e) Find the pdf of U|X.

Question

Let X ∈{1,2} and Y ∈{3,4} be independent random variables with PMF-s: fX(1) = 1 2...

Solutions

Expert Solution

Related Solutions

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

Let X and Y be independent geometric random variables with parameter p. Find the pmf of...

Let X, Y be independent random variables with X ∼ Uniform([1, 5]) and Y ∼ Uniform([2,...

. Let X and Y be a random variables with the joint probability density function fX,Y...

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be independent Poisson random variables with parameters 1 and 2, respectively, compute...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and...

Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z...