Knowing that events X and Y are statistically independent, find the value of A
Y=0 | Y=1 | Marginal probability of X | |
X=0 | 0.5+A | 0.3-A | |
X=1 | 0.1 | 0.1 | |
Marginal probability of Y | 1 |
This question is based on the independence of two random variables.
Knowing that events X and Y are statistically independent, find the value of A Y=0 Y=1...
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
A and B are two statistically independent events, assume the probability of A is 0.4 and the probability of B is 0.5. 1) Determine the P(An B). [The answer should be a number rounded to five decimal places, don't use symbols such as %] 2) Determine the P(AUB). [The answer should be a number rounded to five decimal places, don't use symbols such as %]
Let f(x, y) = kxy, for 0 <x< 1 and 0 <y<1 and 0 elsewhere, a) Find k b) Find marginal pdfs. c) Are X and Y independent? d) Find P(X<0.5, Y>0.5).
Supposc X takes on values 0, 1, and 2 with equal probability and Y takes on value 3 with probability 1/4 and 4 with probability 3/4. If X and Y are independent, find the distributions of (a) X Y. Find fxiy if the marginal densities of X and Y are given by
Supposc X takes on values 0, 1, and 2 with equal probability and Y takes on value 3 with probability 1/4 and 4 with probability 3/4. If X...
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
The joint PDF of random variables X and Y is expressed as
(a) Determine the constant c.
(b) Determine the marginal density function for X.
(c) Determine the marginal density function for Y.
(d) Are X and Y statistically independent?
(e) Determine the probability of P(X ≤ 0.5 | Y = 1).
The joint PDF of random variables X and Y is expressed as certy, 05xs1 and 05ys2 fx.x(x, y) = 10. elsewhere. (a) Determine the constant c. (b) Determine...
Two random variables have the joint density funcitn as follows: f(x,y)=x/y^2 , 0<x<y, 0<y<2 f(x,y)= 0, elsewhere a) Find the marginal distribution of X b)Find the marginal distribution of Y c)Are X and Y statistically independent? (Justify your answer.) d) Find f(x/y)
13. If the events X and Y are independent and P(X) = .4 and P(Y) = 5, what does P(XY) equal? (2) What is the probability of X or Y. (2) What is the conditional probability of Y given X? (2) If the events X and Y are independent and P(X) = .4 and P(Y)-3, what is the conditional probability of Y given X?(2) #4
Two statistically independent random variables, X and Y, are uniformly distributed between 0 and 2 and 0 and 4, respectively. Find and sketch (sketch with all necessary details) the pdf of their sum, Z. Use any information you possess to get to the answer as quickly as possible