1. Let f(x) = c(1- |r|)1|-1,1|(x). (a) Find the constant c that makes f a probability density function. (b) Compute E(X) and Var(X).

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: 5. If f(x) = C x exp(-5x?) for 0 4)

A: The given probability density function is, fx=Cx exp-5x2    ; 0&lt;x&lt;∞0…

Q: If x has probability density function f(x) = 12 x²(1 – x) on [0, 1], find P (;< x< 1). P;< x < 1).

A: We are given: f(x)=12x21-x  a probability density function on [0, 1] We need to evaluate: P12≤X≤1…

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: 4) Suppose X follows Exponential(2), and Y follows Exponential(4). X,Y are independent. (If Z…

A: The answer to the above question is as follows : X~exp(2)f(x)=2e-2x…

Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

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: Let f(x) = 0, C:C x² +1¹ 0, if x ≤ 0 if 0<x<√e-1. if x ≥ √e-1 For what value of c is f(x) a…

A:

Q: Calculate the E(X) when the joint probability density function of X and Y is   fxy(X,Y)=c(X+Y) over…

A: Random variable: A random variable X is a real number that describes the outcome of the random…

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 joint probability density function e-Yi 0 < y2 < Y1 <o∞ f(y1, Y2) elsewhere Find a) E(Y¡Y½) =…

A: GIVEN DATA : Joint probability density function fy1,y2=e-y1 0≤y2≤y1≤∞0 elsewhere TO FIND : (a).…

Q: Solve. Let f(x)= kx for x 2,3,4. Find k so that the function of f (x) satisfies the two properties…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Let X and Y has joint probability density function AX, Y) = 0<x<2, 0<y<2. 16 Find E( X Y ).

A: Solution: From the given information, the joint probability density function of X and Y is

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: Let X and Y has joint probability density function AX, Y) = 11 ^2 e-^, * - A,y ,0<x<∞, 0 <y<∞. Find…

A:

Q: Determine the value of c that makes the function f (x, y) = cxy for 0 < x < 4 and 0 < y < 4…

A: The joint pdf of X and Y is given by f(x, y) = cxy , 0 &lt; x &lt; 4 and 0 &lt; y &lt; 4

Q: If the joint probability density function of X and Y is f(x, y) = e**), 0 < x, 0<y. Are X and Y…

A: Given the joint probability density function of X and Y is fx,y=e-x+y,    x≥0, y≥0

Q: 2. Suppose X and Y have joint probability density function f(x,y,z)= |a(x²+xyz),0<xs1,-1<ys1,1szs2…

A:

Q: a) Suppose that, for-1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂) =…

A: Solution

Q: (4x³ : - Suppose X has probability density function Jx(x)={ 0<x<1. : otherwise

A:

Q: Suppose a probability density function is given by f (x) = Cxe; 0 0 for all r to be 0 there.)

A:

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

A: a.The joint probability density function is,

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: The probability density function on the indicated interval is given by : fx=kx32 ; 4, 9 As we know…

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

A:

Q: b) Find the marginal probability density function of Y, fy (y).

A:

Q: 9. Let the distribution of X for x >0 be 3 xk e-a F(x) = 1 –E k! k=0 What is the density function of…

A: The distribution of X for x&gt;0 is given below: Fx=1-∑k=03xke-xk!

Q: 6. Suppose a college professor never finishes her lecture before the end of the class period, and…

A: We know that the total probability is always 1.Using that we…

Q: Q2-If the density function of X is fx(x) = x = 1,2, ... 0.W S-4 if X is odd What is the probability…

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

Q: 3. Suppose that the probability density function of X is f (x) = 3x², 0<x<1 elsewhere %3D 0,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: 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: Example 26: For a random process having R (t) = ae blt, find the spectral density function, where a…

A:

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

A:

Q: 9- The important properties of the probability density function p(x) was: a- p(x) dx = 0.5 b- P(x)…

A:

Q: 9. Let the distribution of X for x > 0 be 3 xk e-* F(x) = 1 – ) k! k=0 What is the density function…

A: The distribution of X for x&gt;0 is given below: Fx=1-∑k=03xke-xk!

Q: Let Y1,...,Yn constitute a random sample from the probability density function given by Г(20)…

A:

Q: For what value of c is the function {3 [c/x5 if x 2 1 f(x) otherwise a probability density function?

A: Obtain the value of C. The value of C is obtained as follows; Probability Density function:

Q: Let f(x, y) = 2xy 0<x< 1,0 < x + y< 1 and let it equal 0 otherwise . a. Show that f(x,y) is a joint…

A:

Q: At a restaurant, the density function for the time a customer has to wait before being seated is…

A:

Q: Determine the value of e that makes the function f(x, y) = cxy for 0 < x < 4 and 0 < y < 4 satisfies…

A: Solution

Q: (b) The conditional probability density function of Y, given that X=x for some x>0, takes the…

A:

Q: Suppose X and Y have joint probability density function f(x,y,z)= a[x²+xyz),0sxs1,-1sys1,1szs2…

A:

Q: let X and Y have the joint density e (x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are Not…

A: Answer: Stochastically Independent.

Q: b. The random variable X has probability density function, ƒ given by { #(1+x²), 0<I< 3 f(x) = 0,…

A: From the given information, fx=1121+x2, 0&lt;x≤3 Y=3X+1 i) The distribution function of Y: Hy=PY≤y…

Q: Determine the value of c that makes the function f (x,y) = cxy for 0 < x < 4 and 0 < y < 4 satisfies…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.