Give an example of a function F which is the joint probability distribution (not density) function...

Give an example of a function F which is the joint probability distribution (not density) function of a pair of random variables X and Y such that

(a) X and Y are independent and discrete

(b) X and Y are dependent and discrete

(c) X and Y are independent and continuous

(d) X and Y are dependent and continuous

Expert Solution

ANSWER::

NOTE:: I HOPE THIS ANSWER IS HELPFULL TO YOU......**PLEASE SUPPORT ME WITH YOUR RATING......

**PLEASE GIVE ME "LIKE".....ITS VERY IMPORTANT FOR,ME......PLEASE SUPPORT ME .......THANK YOU

orchestra answered 2 years ago

Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y...

Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y (x,y) = 4x/y3 I(0.1)(x), I (1, ∞)(y). Calculate a) P(1/2 < X < 3/4, 0 < Y ≤ 1/3). b) P(Y > 5). c) P(Y > X).

18. Joint Probability Calculations: a) What is a joint probability density function? i. What is an...

18. Joint Probability Calculations: a) What is a joint probability density function? i. What is an example of a discrete joint probability function? ii. What is an example of a continuous joint probability function? b) What are marginal density/mass distribution functions? How can we calculate them from the joint density/mass distribution functions? i. Can you calculate the marginals when the joint space is not a rectangle? (e.g. The space of jpdf[x,y] is 0 < x < y, 0 < y...

Suppose that X and Y have the following joint probability density function. f (x, y) =...

Suppose that X and Y have the following joint probability density function. f (x, y) = (3/394)*y, 0 < x < 8, y > 0, x − 3 < y < x + 3 (a) Find E(XY). (b) Find the covariance between X and Y.

. The joint probability density function of X and Y is given by ?(?, ?) =...

. The joint probability density function of X and Y is given by ?(?, ?) = { ??^2? ?? 0 ≤ ? ≤ 2, 0 ≤ ?, ??? ? + ? ≤ 1 0 ??ℎ?????? (a) Determine the value of c. (b) Find the marginal probability density function of X and Y. (c) Compute ???(?, ?). (d) Compute ???(?^2 + ?). (e) Determine if X and Y are independent

A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random...

A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random variable X . Explain in words, and words only, this property: P ( x a < X < x b ) = P ( x a ≤ X ≤ x b )

Suppose that the distribution of wind velocity, X, is described by the probability density function f(x)...

Suppose that the distribution of wind velocity, X, is described by the probability density function f(x) = (x/σ^2)e^-(x^2/ 2(σ^2)) , x ≥ 0. Suppose that for the distribution of wind velocity in Newcastle, measured in km/hr, σ^2 = 100. (a) In task 1, you showed that the quantile function for this distribution is given by: Q(p) = σ (−2 ln(1 − p))^(1/2), 0 ≤ p < 1 Use this quantile function to generate 100,000 random values from this distribution (when...

Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x)....

Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x). Explain the following issues using diagram (Graphs) a) Relationship between f(x) and F(x) for a continuous variable, b) explaining how a uniform random variable can be used to simulate X via the cumulative distribution function of X, or c) explaining the effect of transformation on a discrete and/or continuous random variable

Derive conditional expectation from joint probability density function.

The joint probability density function for two continuous random variables ?? and ?? is ??(??, ??)...

The joint probability density function for two continuous random variables ?? and ?? is ??(??, ??) = ??(3??2 − ??), 0 < ?? < 1, 0 < ?? < 1. Answer the following: (a) Find the value of ?? such that ??(??, ??) is a valid probability density function. (b) Find the marginal probability density function for ??, ??(??). (c) Find the marginal probability density function for ??, ??(??). (d) Find the conditional probability density function for ??|?? = ??,...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1 for 0 < x < 1, x < y < x + 1. What is the marginal density of X and Y? Use this to compute Var(X) and Var(Y) Compute the expectation E[XY] Use the previous results to compute the correlation Corr (Y, X) Compute the third moment of Y, i.e., E[Y3]

Question