Question

In: Statistics and Probability

The binormal distribution for (X, Y) is defined as the marginal distribution X ∼ N (1,4)...

The binormal distribution for (X, Y) is defined as the marginal distribution X ∼ N (1,4) and conditional distribution Y | X = x ∼ N (1 – x, 1).  Find Pr(X < 1|Y = −1).

Solutions

Expert Solution

The problem is solved by finding the parameters of the binormal distribution and then using the conditional distribution. For further query in above, comment.


Related Solutions

Suppose X and Y are two independent random variables with X~N(1,4) and Y~N(4,6). a. P(X <...
Suppose X and Y are two independent random variables with X~N(1,4) and Y~N(4,6). a. P(X < -1.5). b. P(0.5Y+1 > 5). c. P(-2 < X + Y < 5). d. P(X – Y ≥ 3).
If Y is distributed N(1,4), find Pr(Y>0).
If Y is distributed N(1,4), find Pr(Y>0).
Consider the following payoff table for an evolutionary game: X Y X (0,0) (1,4) Y (4,1)...
Consider the following payoff table for an evolutionary game: X Y X (0,0) (1,4) Y (4,1) (0,0) 1. If we consider this table as a normal form game, in the mixed strategy Nash equilibrium the probability of X is?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6 F. 1/7 G. 1/8 H. 1/9 2. The mixed equilibrium you found is Consider the following payoff table for an evolutionary game: X Y X (3,3) (1,3) Y (3,1) (2,2) 1....
Assume that an operation * is defined as follows: x * y = x' + y...
Assume that an operation * is defined as follows: x * y = x' + y Using Boolean algebra theorems and postulates (don’t use K-maps), check whether the operation * is associative or not?
Given two functions, M(x, y) and N(x, y), suppose that (∂N/∂x − ∂M/∂y)/(M − N) is...
Given two functions, M(x, y) and N(x, y), suppose that (∂N/∂x − ∂M/∂y)/(M − N) is a function of x + y. That is, let f(t) be a function such that f(x + y) = (∂N/∂x − ∂M/∂y)/(M − N) Assume that you can solve the differential equation M dx + N dy = 0 by multiplying by an integrating factor μ that makes it exact and that it can also be written as a function of x + y,...
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...
If the joint probability distribution of X and Y f(x, y) = (x + y)/2
If the joint probability distribution of X and Y f(x, y) = (x + y)/2, x=0,1,2,3; y=0,1,2, Compute the following a. P(X≤2,Y =1) b. P(X>2,Y ≤1) c. P(X>Y) d. P(X+Y=4)
find zero state response y[n+4]-y[n]=x[n], if x[n]= e^-n u[n]
find zero state response y[n+4]-y[n]=x[n], if x[n]= e^-n u[n]
Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution...
Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution formula
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT