. Let a random variable X - U(5,5+0). Based on a single observation X1, find the unbiased estimator of 0.

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=. , find k. O.w

A: Step 1: Given,                            f(x) =1k e-8x0, 0&lt;x&lt;∞ We know that ,…

Q: Given a random variableX, with standard deviationo x, and a random variableY=aX +b, show that if…

A: It is given that, Y = aX + b and the standard deviation of X is, σx.

Q: Suppose a random sample {X}~ i.i.d.(u,02). Define the following estimator 71 2 Ĥ [jxj. n(n+1) j=1…

A: If x is consistent for µ if   E(X) = µ V(x) tends to 0.

Q: Given the normally distributed random variable X with s 1⁄4 10 and P(X<40)= 0.0080,  find u

A:

Q: Suppose for this random variable X we want to compute P(X ≤ 3)

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Q: Let X be a random variable with p.d.f. 4k 1< x<10 f (x) =< find k. O.W

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Q: Suppose that X is a random variable having the following p.d.f. , Find the Mode * ? F(«) = {o**(1 :…

A: Introduction: Suppose, X is a prescribed continuous random variable with probability density…

Q: Let X be a random variable with p.d.f. 1 3k e 4 0<x< 00 f(x) = { find k. O.W

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Q: Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with…

A:

Q: Suppose that X is a binomial random variable with n=300 and p=0.47 Use a normal approximation to…

A:

Q: If a random variable X is defined such that E[(X-1)*]=10and E[(X-2)²]=6, find ux and o?,

A: Consider           EX-12=10    EX2-2X+1=10EX2-2EX+1=10      EX2-2EX=10-1…

Q: Which of the following is equal to Cov (X+ Y, 2X +Y), where X and Y S ? are random variables on a…

A:

Q: A simple random sample of size three x1, X, and x3 is drawn from a population with mean u and…

A: From the given information, 1) An estimator are said to be unbiased if E(x) =µ. Hence, it is…

Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: Let X1, X2, ..., Xn ~ exp(A) be a random sample. Show that X is sufficient for 1/A.

A: Given:  X1,x2,.....xn from exponential distribution with parameters lambda  Then to show that xbar…

Q: Prove that if M(t) is the MGF of a random variable X, then the MGF of a + bX is e^at M (bt)

A:

Q: NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of…

A: From the provided information, 1 in 20 children in United States have a food allergy of some sort…

Q: Suppose that X is a binomial random variable with n=230 and p=0.48. Use a normal approximation to…

A: Given data, n=230 p=0.48 P(X≥100) = ?

Q: Let X be a random variable with p.d.f. 2e-2x 0<x<00 f (x) =• , find E(e 2*) O.w

A: Given, the probability distribution function of a random variable X- fx=2e-2x  ; 0&lt;x&lt;∞0…

Q: (30) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) = { , find E(e*) O.w

A: It is given X is a random variable with pdf f(x) = 2e-2x,0&lt;x&lt;∞0,otherwise

Q: (27) Let X be a random variable with p.d.f. 3e-3x 0 <x< 00 f(x) =. , find E(x) O.W

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Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: Let X be a random variable with the function, -(x-4) for x > , Let f (x)={ elsewhere. Derive u and…

A: Given that X is a random variable with probability density function; f(x)=e-(x-λ), for x&gt;λ0,…

Q: Let the following simple random sample X1, X2, X11 following: 1. Binomial pmf. (11, ¾); 2. Uniform…

A: The pmf of discrete uniform distribution is given by p(y)=1n=111 The cdf of discrete uniform…

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

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Q: Suppose that X is a random variable * ? having the following p.d.f. , Find Var(x) { 2(1 – x) 0 < x <…

A: Given: f(x)=2(1-x) , 0&lt;x&lt;1 The formula to compute the mean is: V(x)=∫x2fx dx-∫xfx dx2

Q: Find P(X = 3) if the mean of the Poisson random variable is A = 11. %3D 0.002021 0.271801 0.003705…

A:

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: Given,f(x)=k(x-x4)     ; 0≤X≤10                 ; other wise

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=- , find k. O.w

A: Given: The probability density function of the random variable X is given as:…

Q: Let X be a random variable with p.d.f. 3k e 4 0<x<∞ f(x) =- find k. O.W

A: given p.d.f. is                                                     f(x)=3ke-14x   ; 0&lt;x&lt;∞0…

Q: The moment generating function for a random variable X is: 5 21 1 Mr(t) = 8 e' + 4 8 | Calculate…

A:

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

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Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: IÊ X is havingpdf a Continous random´variable shown in Fig- as PXt OFind the constant k

A: Given : If X is a random variable having the following pdf : The pdf contains two trapeziums ,…

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

A: Random Variable: A random variable is a real valued function that assign a real number to each…

Q: :A random sample of 100 observations from a population known to be non-normal yielded the sample…

A: From the provided information, Sample size (n) = 100 Sample mean (x̅) = 182 Sample variance (s2) =…

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=< , find k. O.w

A: Given information: It was stated that X is a random variable. The probability distribution…

Q: Let xbe a Geometric random variable with p%3= 0.6. Find the mgf at zero MO)

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Q: *11. Show that for the two-tailed test, the p-value is: Vn(Ỹ – 60) 2 1- 0

A:

Q: Suppose that P{X = a} = p, P{X = b} = 1 – p, %3D %3D a. Show that X-b is a Bernoulli random variable…

A: The probability at X=a is p. The probability at X=b is 1-p.

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)30.5, P(2)=0.2 and…

A: The discrete random variable X takes only three values 0, 2, and 3. The probabilities are P0=0.5,…

Q: Let X be a random variable with p.d.f. 2k x= 1,2,3 (x-1)! f(x)=• , find (1) k (2) E(2x) O.w

A: Solution: 32. From the given information, the probability density function of X is

Q: Find P(X = 3) if the mean of the Poisson random variable is A = 10. O 0.007567 0.004540 0.000067…

A: the question is related to Poisson distribution probability formula for Poisson probability: P(X =…

Q: Let the following simple random sample X1. X2, · .X11 following: 1. Binomial pmf. (11, ); 2. Uniform…

A: Since the question has multiple sub parts we will solve the first three sub parts. Please resend the…

Q: Find P(X = 3) if the mean of the Poisson random variable is A = 3. O 0.059791 0.224046 O 0.271801 O…

A:

Q: Suppose X and S² are calculated from a random sample X₁,..., Xn drawn from a population with finite…

A:

Q: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…