7. If the r.v.'s X and Y have bivariate normal distribution with parameters ₁ = 3.2, µ2 = 1.44, 0₁ =12, 02 = 16 and p = 0.7, determine the following quantities:(a) E(X), E(Y), Var(X), Var(Y), p(X, Y), and Cov(X, Y).(b) the distribution of X and the distribution of Y.(c) the probabilities P(0.8 < X < 4.2), P(Y > 14).(d) the conditional distribution of Y, given X = 3.8.(e) the conditional distribution of X, given X = 10.(f) the probabilities P(X > 3.2|Y = 10), P(Y < 12|X = 3.8).(g) E(X|Y = 10), E(Y|X = 3.8), Var(X|Y = 10), Var(Y|X = 3.8).

"Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Answered: 7. If the r.v.'s X and Y have bivariate…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

X is normally distributed with mean 2 and standard deviation 3. Y is normally distributed with mean 4 and standard deviation 4. What is P(Y > X)? (a) If X and Y are independent? (b) If X, Y have a multivariate normal distribution, and Cov(X, Y ) = 2?
Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)
Assume X_1, X_2, .....X_n are random samples from X~Exponential(θ).1) Find the MLE estimator of θ .
In an Omani factory, a machine that produces "W-product" has been set so that the true average diameter of the "W-product" it produces is 0.602 in. If its diameter is within 0.04 in. of this target value, this is acceptable. Suppose, however, that the setting has changed during the course of production, so that the products have normally distributed diameters with mean value 0.601 in. and standard deviation 0.002 in. What percentage of the "W-product" produced will not be acceptable
Let x be a continuous random variable that is normally distributed with a mean of 25 and astandard deviation of 4. Find the area(a) between x =25 and x =32 (b) between x =18 and x = 34
Let X be a standard normal RV. Suppose Y = 2X+3 and Z = -X+6. a) Find the covariance between Y and Z b) Find the correlation coefficient between Y and Z
Consider the continuous random variable X = the weight in pounds of a randomly selected newborn baby born in the United States last year. Suppose that X can be modeled with a normal distribution with mean μ = 7.57 and standard deviation σ= 1.26. If the standard deviation were σ = 1.06 instead, how would that change the graph of the pdf of X?
A metal company is supplying its product to a manufacturer of washing appliances that has specified that the outside diameter be 0.255 + 0.028 inch. Fifty samples of n = 5 units show that the process is in good statistical control, the diameters are normally distributed, and that μx and σx for the process are 0.260 and 0.02 inch, respectively. a) What percent of the product made by this process is within the specifications? Answer in 2 decimal placesb) If the process variability was reduced by about half (i.e., σx changed to 0.01 inch), what percent of the product made by this process is within the specifications? Answer in 2 decimal places.
Suppose that Z given Y = y has a normal dlistibution with mean zero and variance y^2 and that Y has a x^2 distribution with v degrees of freedom. find the variance of W = Z/sqrt(Y).
If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its standard deviation?
If X and Y have a bivariate normal distribution andU = X + Y and V = X − Y, find an expression for thecorrelation coefficient of U and V.
Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS