14. A random variable X has probably density function fx) = k for –3 < x< 3 = 0 otherwise, where k is a constant. Find the value of k, expectation of X and P(I XI< 2, I XI > 1).

Q: Suppose there is a random variable X whose probability density function has the form (shown in…

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Q: SV) ="(3y² Sh(3y² + 2) ; -2<ys2 0; otherwise

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Q: b) Let X₁, X₂, X3X be a random sample of n from population X distributed with the following…

A: Given Xi~N(0,θ) Mean=E(X)=0, V(X)=θ  Note: According to Bartleby guidelines expert solve only one…

Q: Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random…

A: At first remind that                                      Independent ⇒UncorrelatedBut, Uncorrelated…

Q: Let X and Y be independent random variables. Suppose X is of type X= 10, exponential with parameter…

A: Given  X and Y are independent and follows exponential distribution with λ=10

Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95%…

A: Firstly we have to find the MLE of the parameter and then variance to get the required confidence…

Q: Q3// let X and Y have the joint probability distribution function as : . (x, y) (1,1) (1,2) (1,3)…

A: Given that Joint probability distribution function of X and Y (x,y) (1,1) (1,2) (1,3) (2,1) (2,2)…

Q: Exercise 23. Let X be a random variable having the uniform distribution on the interval (0,0+ 1), 0…

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Q: Let Y₁, Y2, ..., Yn be a random sample whose probability density function is given by {G/B² € 7. 684…

A: Given Y1, Y2, . . . ,Yn be a random sample with pdf : fy; β=y36β4e-yβ , 0&lt;y&lt;∞ and β&gt;0…

Q: For N random variables, show that, (W,t..un) Px1..... <Ox1. x, (0,.0) =1 .......

A: Answer: For the given data,

Q: 10. Let Yı, Y2., Yn denote a random sample from the probability density function given by (0+1)y", 0…

A: Given: fy|θ=θ+1yθ,      0&lt;y&lt;1, θ&gt;-10,                 elsewhere The maximum likelihood…

Q: Let Y,,Y,.,Y, be a random sample of size n from the gamma, distribution with probability density…

A: the probability distribution function is given by fy(y,θ) =1(r-1)!θyyr-1 e-yθ ,y&gt;0 the likelihood…

Q: i) Derive the standard error of B, se (B) = 0.0009, using MLE approach. ii) Find an approximate 95%…

A: Firstly it is required to determine the MLE of the parameter and then the variance to get the…

Q: (4) If X is a continuous random variable with p. d. f. (X) 1 f(x) = }6 ,0<x< 3 12 ,othewise The…

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Q: Let X be a continuous random variable with PDF 2e*,0 3).

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Q: (b) Assume that Y₁, Y₂, ..., Yn are independent normal random variables with mean μ = B₁ + B₁x₂ and…

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Q: 3. Let X be a random variable that is uniformly distributed on the interval (a, b). Find its moment…

A: Moment Generating Function for a random variable X is given by,  E(etX) = ∫-∞∞etxf(x) dx where f(x)…

Q: 7. Find the expected value of the random variable Y whose probability density is given by f(y) = 0…

A: Given that: Probability density function of Y: fy=18y+1      for 2&lt;y&lt;40…

Q: Let X and Y be two jointly continuous random variables. Let Z = X +Y. Show that F2(=) = FxIr(V=- v°…

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Q: Let Y₁, Y2, ..., Yn denote a random sample from the probability density function (0+1)yº, 0 −1,…

A: The first moment of Y about the origin based on the given density function&amp;nbsp; is:Let  be the…

Q: 7) Allow a continuous probability distribution to be defined as f(x) = x/2 for the range 0 sxs2. %3D…

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Q: Let X = (X,,X,,..., X„) be a random sample with size n taken from population has probability density…

A: We want to prove that U=min(X) is the sufficient for θ.

Q: For the given probability distribution, X f(x,y) 1 2 5 0.25 0.2 y 10 0.2 0.15 15 0.15 0.05 Determine…

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Q: c) P(2 1)

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Q: 2. Let Y,, Y2, .,Y, be random variables sample from a distributions with probability .... density…

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Q: Let X,, X2,.. ,X, be a random sample from a distribution with density function if x 20 -e f(x; 0)…

A: The answer is given using the concept of maximum likelihood. please find step by step solution…

Q: Find the expected value and variance of the random variableX whose density function is f(x) =…

A: Given:  fx=12x0.5i.e fx=12x12      ∵0.5=12

Q: The continuous random variable XX has a probability density function (pdf) given by Part(d) Find…

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Q: 25. Obtain the maximum likelihood estimates for a and B in terms of the sample observations x1, x2,…

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Q: (47) Let X b(8, -) find E(5+6x) and distribution function.

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Q: Let  X ~ Bernoulli (p). let Y be some discrete random variable. Know that Y is independent of X.…

A: Let X ~ Bernoulli (p) .Then E(X) = p and V(X) = p (1-p).

Q: The joint probability density function (pdf) of the random variables X and Y is (x+2y), 0sx, ys1…

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Q: Q3// let X and Y have the joint probability distribution function as : . (x, y) (1,1) (1,2) (1,3)…

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Q: i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95%…

A: Firstly it is required to determine the MLE of the parameter and then the variance to get the…

Q: We have a random variable X that is uniformly distributed on interval [-1,2]. Let Y = |X| - 1. We…

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Q: À continuous random variableX has a probability density function (p.d.f) given by f(X)=K(10-X)(X-40)…

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