Show that the following are probability density functions (pdf's):
Q: x (10-x) Q1. Show that f(x): ;0<x < 10; is a probability density function. 5000
A: To be a probability density function, the sum of all f(x) must be 1. so we must…
Q: Exercise 3.3 Suppose that the probability density function of X is 0 2/3). 0,
A:
Q: e) What is the cumulative density function of X?
A: Solution-: Given: a=5, b=50 Let, X- be the waiting time for the light to turn green in seconds…
Q: fxy(x, y)20. A joint probability density function is always non-negative.
A:
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<x<3,0<y<3
Q: Determine the value of c for which the function below will be a probability density functi So(8x' -…
A: Here given thatf(x)=c8x3-x4 ; 0≤x≤80 ; other
Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…
A: To find: The value of k that make the function fx a probability density function: Given: The…
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 (10-x) Q1. Show that f (x) = ;0<x< 10; is a probability density function. 5000
A: To prove that f(x) is a probability density function, we need to show that f(x) adds up to 1.…
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: Show that the following are probability density functions (pdf’s): b. f2 (x) = 2e −2x I(0,∞)(x)
A:
Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…
A:
Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…
A: The probability density function is given as f(x) = 4x0≤x≤124-4x12<x≤10otherwise The cummulative…
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: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.
A: Given, fx=kx2To find : Determine tha value of k that makes fx a probability density…
Q: Consider the probability density function if x 1. 2x4 Find E(X). Select one: | -IN -|0 O O O O
A: Obtain the expected value of E(X). The expected value of E(X) is obtained below as follows: From…
Q: 1) Show that the given function is a pdf (Probability Density Function) Q6 f(x) = = e7, [0, In4]
A: The probability density function is ∫-∞∞f(x)dx=1 if Pa≤x≤b=∫abf(x)dx and f(x)≥0 if the function is a…
Q: determine which are probability density functions and justify your answer. 1. ƒ(x) = 1/18 x over…
A: For a function to be a probability density function (p.d.f) it must fulfil the conditions;a)Function…
Q: Show that if the exponentially decreasing function if x 0 f(x) = LAe is a probability density…
A: Given: fx=0 ; if x<0Ae-cx ; if x≥0 For a probability density function f(x).…
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: (4x³ : - Suppose X has probability density function Jx(x)={ 0<x<1. : otherwise
A:
Q: determine which are probability density functionsand justify your answer.
A:
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: Is the probability density function a valid PDF? * if x 1 F(x) = x2 +=x3/2 %3D ON/30
A: the probability density function i.e., pdf of a random variable X is denoted by f(x) and the…
Q: Let X and Y have the following joint probability density function(pdf): if 0 < x < 1, 1<y<2 f(1, y)…
A: Consider the following pdf- f(x,y)=c.x2y,0<x<1, 1<y<20,otherwise EX|Y=∫01x f(x,y)dxf(y)
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: Let X be a random variable with probability density function 3 -x², -1 < x < 1 2 Which of the…
A:
Q: The probability density function of Y = 5X + 3 is:
A: To obtain the probability density function of Y=5X+3, we will use the transformation method.
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: 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: Show that the following are probability density functions (pdf's): b. f2(x) = 2e-2*I(0,00)(x) %3D
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: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…
A: Consider the function: fx=kx12, x∈1, 4 and, for all other values of x, fx=0. Thus, fx=0,x∈-∞,…
Q: Let X be a random variable with probability density function fx(x) given by fx(x)= 0. (2e-2 for x20…
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: If you know that the following function is joint probability density functio f(x,y) = {8xy* {8xy* 0…
A: Given that the density function is, f(x,y)=8xy4, 0≤x≤y≤t The value of t is obtained by using the…
Q: Show that the standard normal probability density function f(x) has points of inflection when x =…
A: Concept - Inflection point is obtained at f''(x) = 0.Given function f(x) - f(x) =…
Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?
A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.
Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…
A: Given: ƒ(x) = kx3; [2, 4] A probability density function equals 1 for sum of all range of values.
Q: 4 Consider the following two functions, each having an unknown parameter c. Sc(a2 + 4x + 7) -5<x < 5…
A: Given, The following two functions: f(x) = c(x2 +…
Q: Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?
A: Answer:- Given that, X is exponentially distributed with mean 2.
Q: Suppose that the joint probability density function of X and Y is fxy(x,y) = 2(x² - y?) e-2x, for…
A:
Q: Which of the following is Not a property of probability a density function f(x)?
A: Properties of probability density function, f(x) :
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…
Q: Show that the following are the probability density functions: fi(x) = e-*I(0,00)(x) f2(x) =…
A: To prove that f(x) is a pdf, we must show that f(x) >= 0 for all x and, using I[a, b] for the…
Q: Show that the f(x) = 12x(1 - x)^2 is a probability density function over the interval [0, 1]. %3D
A: We know that, if there is a function f(x) and the integration of f(x) over the given range is 1.…
Show that the following are probability density
a. f1
(x) = e
−x
I(0,∞)
(x)
Step by step
Solved in 2 steps with 2 images
- Show that the following are probability density functions (pdf’s):The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2 for x in [0,∞). Find the probability that a randomly selected laptop battery will last between 2 and 5 years?suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
- Suppose the joint probability density function (pdf) of continuous random variables X, Y isVerify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.How to verify that this is function is a probability density function? Also, how would you find P(x<3) Let f(x) = { pi/10 sin (pix/5) if 0<x<5 0 if x<0 or x>5
- Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.