(a) the joint probability function f(x, y),

Q: 15 fxy(x,y)= 32 is a joint probability density function over the range 0<x<2 and 0<y<x. Find E(XY).

A:

Q: 3. Suppose that the probability density function of X is [3x?, lo, 0 < x< 1 f(x) = otherwise…

A:

Q: The joint probability density function of X and Y is given by fxx(2, y) = }(x + y) for 0 1.5|X < 1)…

A: Given : The joint probability density function of X and Y is given by; fX,Yx,y=18x+y for…

Q: What is the value of the constant c for p(x) to qualify as a probability mass function?…

A: We want to find the value of c

Q: Find the conditional expectation E(Y/X=0.47) if the joint probability density function of the random…

A: We want to find conditional expectation.

Q: If fx) is a probability mass function then ) =1. i--2 True False

A: In the given problem we have a pmf.  And we have answer either true or false.

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: Find the joint probability density function fu,v of U =X² – 1 and V = 2Y. -

A: We will use Jacobian method of transformation to find the joint pdf of U and V.

Q: Let X and Y has joint probability density function AX, Y) = ترفير ,0 <x<2,0<y<2. Find V(X).

A: Let X and Y has joint PDF ,  f(X,Y)=x3y316 ; 0&lt;x&lt;2 , 0&lt;y&lt;2. Therefore the value of X,…

Q: The joint probability density function of X and Y is given by 6 ху fxy (x, y) = (x² +) 0 <x < 1, 0…

A: Given information: The two random variables X and Y has a joint density function as: fXYx,y=67x2+xy2…

Q: fxy(x, y)20. A joint probability density function is always non-negative.

A:

Q: 7. If the joint probability density function of X and Y is 1 if 0 < x < 1; 0 < y < 1 f(x, y)…

A:

Q: 3- If f(x)= is the probability density function for a random variable that can take on the values x…

A:

Q: For the continuous probability function f(x) = 2kx² e¬* when x > 0 a. value of k %3D b. mean

A: Integration of continuous random variable is 1.

Q: et it be the probability density function. [ f(x2= n-x 2(1-2). ax Let it be Y = e x=0,1,2, So E(Y)…

A: Solution

Q: (a) Explain why P(X ≤x) #1, for every x. (b) Find a and b. (c) Find the probability density function…

A:

Q: The joint probability function for X and Yis given below. E(2X + 3Y) is 1. 0.25 0.35 0.23 0.17

A: We have given that the joint probability distribution of X and Y.

Q: X and Y have joint probability density function f(x, y) = ye 0 10), and P(Y < X). %3D fo

A: Let X and Y be two continuous random variables falling in interval -∞,∞ with joint density function…

Q: If the probability density function of X is : f(x) = e-x (1+e*)2 en what is the probability density…

A: It is an important part of statistics. It is widely used.

Q: The random variable X has a probability density function given by: k 1<x< 10 f(x) =} Vx- otherwise…

A:

Q: Is f(r) a legitimate probability mass function? E(1- p)*-'p =p+ (1 – p)p+ (1 – p)°p+ • … 2 1 r=1

A: To be a legitimate probability mass function we must have all the probability between 0 and 1.And…

Q: A joint probability density function is given by f(x,y) = x+y, 0&lt;=x,y&lt;=1. Find conditional…

A: A joint probability density function is given by,

Q: Let X and Y has joint probability density function AX, Y) = *7 ,0<x<2, 0 <y<2. x y Find E( X + Y)

A: Given a joint probability density function of X and Y , we need to find E( X+Y)

Q: Give the two conditions that a probability density function for [a, b] must satisfy.

A: The probability density function f(x) lies in close interval a to b.

Q: Find the joint probability function of (X,Y) where

A: Provided information is, two cards are drawn at random from a box which has 5 cards numbered 1, 2,…

Q: a. Find E(X) b. Find E(Y) c. Find E(XY)

A: a.The joint probability density function is,

Q: 3. Find the value of k so that f(x) for 1 < x < 2 is a probability density function. (x + 1)?

A:

Q: a- Find the joint probability density function of (X(1), X(n).

A: Given:  x1,x2,.....xn be tye iid frim uniform (?, ?+1) Then to find joint pdf of X(1) and X(n) order…

Q: Let the random variables X and Y have the joint probability density function f(x, y) =5…

A:

Q: (b) Find the probability density function of Y= X

A: A random variable X has a probability density function: f(x)=0; x&lt;012; 0≤x≤112x2; 1&lt;x&lt;∞

Q: The probability density function of X is f(x) = for 0 <= x < 10, then 10 10 P(X +2 7) is:

A: Since , the probability density function of X is given by , Our aim is to find the ​​​​​​​

Q: a) What must c be for the function to be a probability density function? b) Calculate F(1).

A: c can be calculated as:

Q: Is f(x) a legitimate probability mass function? 1- p)*-1p = p+(1 – p)p + (1 – p)°p +. 1 %3D x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: Find  EY|X(y|x=2)

A: Given joint probability density function

Q: 2- If the probability density function of X is : f(x) : -00 <x < ∞ (1+e-*)2 1 then what is the…

A: The distribution function of y is given by…

Q: A random variable X has a probability density function 0; x < 0, 0≤x≤1, 1<x<∞0. f(x)= { 22

A: a) Given information: fx=0, x&lt;012, 0≤x≤112x2, 1&lt;x&lt;∞

Q: The function f(x) = 7x for x = 1,2,4 and zero otherwise, is a probability mass function.

A: Here use basic of Probability mass function

Q: 6. Given the joint probability density function f(x, y)=10xy, 0<x<y<l, find P(X+Y <1).

A:

Q: If f(x)= O<x<5 is a probability density function and m is unknown real number (constant), then m=

A:

Q: If X ~ U(3, 15), what is the probability density function for this distribution?

A:

Q: If the probability density function of random variable X is given by: f(x) = {o." ( kx? + x, x €…

A: Given ,f(x)=kx2+x  ;  x∈0,10           ;  otherwise

Q: Could fx(x) be a probability density function? If so, determine C.

A: Probability distribution function is very useful . It is of utmost importance in statistics .

Q: B) The probability density function for the random variable X is given by 0<x<3 f(x) ={(25 – x²), 0,…

A: Given function is,  f(x)=x2, 0&lt;x&lt;3(25-x2), 3≤x&lt;60, otherwise

Q: Why is P(X = c) = 0 for any number c in the domain of a probability density function?

A: There are two types of function in probability. One is for Discrete random variable and the other is…

Q: Find the moment generating function, mean and variance of X if the probability mass function is f(x)…

A: Let X be a random variable with probability function (probability mass function or probability…

Q: Let the joint probability density function of the continuous random variables X and Y be f(x, y) = 5…

A: Given that X≤YAnd given that 0≤Y≤1 So, we have:  0≤X≤Y≤1

Q: Q3 If the joint probability density function of X and Y is given by 0 < x < ∞, 0 < y< o∞ f(x, y) =…

A: Ans . Here for calculation of E [ X/Y=y ]  ,  we first calculate marginal distribution of  Y  then…