Show all necessary solutions. 1. Let f(r) = c(1– |2|)1|-1,1(21). (a) Find the constant c that makes f a probability density function. (b) Compute E(X) and Var(X).
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Q: x (10-x) Q1. Show that f(x): ;0<x < 10; is a probability density function. 5000
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A: The answer to the above question is as follows : X~exp(2)f(x)=2e-2x…
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A: The joint probability density function is, fX,Y=x2y281,0<x<3,0<y<3
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Q: 3. Consider the function f (x) = B - x/4 for 1 s x s 2 and f (x) = 0 otherwise. Determine the value…
A: Explanation of the answer is as follows
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A: Since you have asked multiple question, we will solve the first question for you. If you want any…
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Q: 5.1.8 WP Determine the value of c that makes the function f(x, y) = c(x+ y) a joint probability…
A: As per our guidelines, we can answer the first three subparts, Kindly repost the others for answers.
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)
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A: From the definition: The function f is a probability density function of a random variable x in the…
Q: 2. Suppose X and Y have joint probability density function f(x,y,z)= |a(x²+xyz),0<xs1,-1<ys1,1szs2…
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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)?
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Q: A. Consider the probability density function f (x) = kx²e* 0 sxs2 %3D otherwise %3D Find the…
A: ∫02k x2exdx =1kx2ex-2xex+2ex02=1k(2 e2-2)=1k=12(e2-1)=112.77 k=112.77811
Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…
A: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…
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Q: Let X and Y has joint probability density function AX, Y) = , 0<x<2,0<y<2. 16 Find V(X). TTT Arial
A: Solution: From the given information, the joint probability density function of X and Y is
Q: x' (10-x) Q1. Show that f (x) = ;0<x < 10; is a probability density function. %3D 5000
A: Given : f(x) = x310-x5000 ; 0 ≤ x ≤ 10
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A: Hey there! Thank you for posting the question. Since there are two questions posted, we will answer…
Q: 6. Given the joint probability density function f(x, y)=10xy, 0<x<y<l, find P(X+Y <1).
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Q: 1. 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 posted multiple questions, I have answered only one f(x)=kx for x=2,3,40,…
Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…
A: Given probability density function is: ƒ(x) = kx2 ; Interval ; [-1, 2]
Q: a) Suppose that, for -1 < a < 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂)…
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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: 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: Suppose that the probability density function of X is 3x 0<x<1 elsewhere Determine the P (X<1/3), P…
A: Since you have asked multiple questions, we will solve first question for you. If you want any…
Q: 1. Suppose we have a function K f(x) in [1,2]. (a) Determine the value of the constant K that makes…
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Q: 1. Suppose that the random variables x, Y , and z have the joint probability density function…
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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.
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Q: 3) The probability density function is f(x) = 2e-kx X>0 Find the value of k.
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Q: Suppose X and Y have joint probability density function f(x,y,z)= a[x²+xyz),0sxs1,-1sys1,1szs2…
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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: b. The random variable X has probability density function, ƒ given by { #(1+x²), 0<I< 3 f(x) = 0,…
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Q: a) Suppose that, for -1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂)…
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- For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)Suppose that Y1, . . . , Yn is a random sample from a population whose density function isf X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.
- X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2Let X1, ...., Xn be a random sample from a population with θ unknown and given by the density f(x; θ) = ( 1 2θ √2 x e − √2 x θ if x > 0 0 if x ≤ 0 1. Show that E(X) = 2θ 2 and E( √2 X) = θ (Hint: you may use that R ∞ 0 e −z z α−1dz = (α − 1)! for every α ∈ N). 2. Show that the statistic θbn := 1 n Xn i=1 p2 Xi (1) is an unbiased estimator of θ. 3. Give the definition of a consistent estimator. 4. Show that the estimator θbn given in relation (1) is a consistent estimator of θ. 5. Show that the estimator θbn is a minimum variance estimator of θ. (Hint: use the Cramer-Rao inequality given by var(θb) ≥ 1 nE ∂ ln(f(X;θ) ∂θ 2Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF, denoted f, is given by f ( x ) = c ( 25 − x^2 ) , − 5 ≤ x ≤ 5 , and where c is a positive normalizing constant. What is the expected value of X^2?
- Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.This revolves around the subject of linear models. The given problem is: Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y. My attempt at the problem is shown below. Is my solution correct? If not, why? I figured that the 2 in X + 2Y was a constant, so it could be ignored.Suppose that the joint density function of the random variables X and Y is f(x,y)=k(1+2y), if 1<x<13 and 0<y<1, and f(x,y)=0, otherwise. Show that the marginal distribution of X is g(x)=c, if 1<x<13, and g(x)=0 otherwise. Enter the value of c. Hint: Of course, first, you need to find the value of k. Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03. (Do NOT use decimal comma; 0,03 would be wrong.)
- Let X1, . . . , Xn be iid with pdf f(x) = 1 x √ 2πθ2 e − (log(x)−θ1) 2 2θ2 , −∞ < x < ∞, and unknown parameters θ1 and θ2. Find the maximum likelihood estimators for θ1 and θ2, respectivelyIf two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)