Example 2.8.3 Suppose X has the geometric distribution with some parameter p which is un- known. Suppose a particular value k for X is observed. Find the maximum likelihood estimate, PML-

Q: If X₁, X₂,..., Xn are the values of a random sample from an exponential population, find the maximum…

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Q: If x1, x2, . . . , xn are the values of a random sample from a normal population with the known…

A: Solution

Q: 7-46. Let X be a random variable with the following prob- ability distribution: J(0+1) xº, 0<xs1…

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Q: The cumulative distribution function F(x) of a random variable X is given by 0, -8 <x<-1 0.2, 0.8,…

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Q: Find u and o for the binomial distribution with n = 676 and p = 0.7. Find the minimum value that is…

A: Let X follows binomial distribution with parameters(n = 676, p = 0.7) The values of mean and…

Q: Assume x follow to binominal with p=4/5 and p=1/5 and n=5 , Find maximum likelihood estimator.

A: X~Binomial (n,p)p(x)=nxpxqn-x Likelihood function  L(p) = ∏i=1nnxp∑xiq∑n-∑xinL(p)=k p∑xiqn2-∑xi…

Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: Suppose that Xi,i =1,2,...,n have an Exponential distribution with parameter delta. a) Find maximum…

A: To get the maximum likelihood estimator, we maximize the likelihood function. To an estimator T be…

Q: Suppose that X1,..., X, form a random sample from an exponential-distribu- ton for which the value…

A: Mle is that value of parameter which maximize the likelihood.

Q: A hypothesis test is to be performed for a population mean with null hypothesis H: u=. The test…

A: Given data: Significance level = 0.01 Two tailed test We use  Z-distribution

Q: Show that the mean of a random sample of size n from an exponential population is a minimum variance…

A: Let X1, X2, …, Xn denote random sample from exponential distribution with θ. The probability density…

Q: f(t; B₁, B₂) = B1 B₂ · (e-P₁² - e-B₂¹) - B₂ - B₁

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Q: Let X be a geometric distribution function with px(n) = p(1 - p)n-¹. Find the expected value and the…

A: P(X=x)=p(1−p)x−1;x=1,2,3,...

Q: Example 2.8.3 Suppose X has the geometric distribution with some parameter p which is un- known.…

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Q: 4. Suppose that Y₁, Y₂, ..., Y is a random sample of size m from Gamma (a = 3,ß = 0), where 0 is not…

A: Given Y1,Y2,..,Yn be the random sample

Q: Assume I observe 3 data points x1, x2, and x3 drawn independently from the same unknown probability.…

A: From given data we have : Prx1|M=0.5,Prx2|M=0.1,Prx3|M=0.2.

Q: If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population…

A: Minimum varience of z=w*x1bar+(1-w)*x2bar is =sigma^2/(n-1+n2)

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: All random samples of size n = 9 are selected from a normal population with u = 55 and o = 10, and…

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Q: the maximum likelihood estimator of a random variable x with uniform distribution U(0, 0), 0 =…

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Q: The lifetime of a machine part has a continuous distribution: Osxs 40 fx(x) = { (10 + x)² else a.…

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Q: If has a Poisson distribution such that P(X 21)=0.8646 then then the variance of is equal to

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Q: Suppose that Y₁, Y₂,..., Y is a random sample of size m from Gamma (a = 3,ß= 0), where 8 is not…

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Q: a) The probability that X1 – X2 exceeds 3. b) The probability that 4.9 < X1 - X2 < 5.9.

A: Let , X1→N(μ1=75 , σ1=9) , n1=15 and X2→N(μ2=69 , σ2=15) , n2=9 and  By using central limit theorem…

Q: Show that the mean of a random sample of size n from an exponential population is a minimum variance…

A: Show that the mean  of the random sample of size n from an exponential population is a minimum…

Q: It is assumed that X has a Poisson distribution with some parameter A with A 20, but the value of A…

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Q: Question 3. Let X₁, Xn be a random sample from a distribution with the pdf given by ƒ₁₁x(x) = ¼ exp…

A: Solution

Q: 7. (a) Let x1, X2, , Xn be a random sample from the uniform distribution -0, dsewhere .... with…

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Q: Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 5.

A: We have given that.   X~N( μ , ?^2 )   μ =30 , ? =5   Z-score =( x - μ )/?