Consider two independent random samples x_(1),x_(2),dots,x_(n) and Y_(1),Y_(2),dots,Y_(n) taken from \Gamma (k,\lambda _(1)) and \Gamma (k,\lambda _(2)), re- spectively, where \lambda _(1) and \lambda _(2) are the scale parameters for the dis- tributions. Assume that k is known. Show that the lower and upper limits of the confidence interval of (\lambda _(1))\ (\lambda _(2)) interval can be expressed as functions of the quantiles of the F distribution.

Q: Find the distribution of W = X^2 when X is Normally distributed with mean = 0 and variance = 4

A:

Q: Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the…

A: From the given information, Consider, X and Y be independent random variables,…

Q: A researcher collected data on the cholesterol level, CC, and the age, AA, of 24 people selected at…

A: Given hypothesis ,   H0 : β = 0 H1 : β ≠0 The test statistic to test the hypotheses for slope is ,…

Q: Suppose IQ scores were obtained for 20 randomly seleceted sets of twins. The 20 pairs of…

A: The 20 pairs of measurements yield x=101.75, y=102.3, r= 0.909, p value= 0.000, and Y (with the ^…

Q: Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i +…

A: Step 1:

Q: A study of 25 online jewelry retailers was done to find the statistical relationship between the…

A: In this case, the least-squares regression line is ŷ = –6047.75 + 11975.14x, where x is the weight…

Q: Let X1,...,Xn be a sample from normal with mean theta and variance 1. Construct an unbiased…

A: We are given a random sample X1, X2, ..., Xn from a normal distribution with mean θ and variance 1.…

Q: Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)

A:

Q: Assume that variables xx and yy have a significant correlation, and that the line of best fit has…

A: Given ,  The variables x and y have a significant correlation. The line of best fit is,  ( Use…

Q: A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a…

A: From the provided information, Sample size (n) = 23 Sample variance (s2) = 53.3 Population variance…

Q: Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of…

A: Since the P-value is 0.000, we reject the null hypothesis that ρ=0. That is, there is significant…

Q: What is the correlation between x

A:

Q: n=13, sum x=120, sum y=340, sum xy=3970, Sigma x^ 2 =1320, Sigma y^ 2 =255555 Calculate the linear…

A: Given n=13, sum x=120, sum y=340, sum xy=3970, Sigma x^ 2 =1320, Sigma y^ 2 =255555

Q: The following is the summary of a sample data collected on n=10 students on x= # of hours spent…

A: We have to calculate MSE for regression of y on x

Q: Below are histograms for three lists of data (imagine the sample is very large and the rectangles re…

A:

Q: Let X1,..,Xn be a random sample from Unif(0, 0+1). Let ô, = X - 62 = X(n) - %3D n+1 Find the…

A:

Q: Let X1,…,Xn be i.i.d. Exp(λ) random variables, where λ is unknown.What is the variance and quadratic…

A: The pdf of min (xi) is as follows: Thus, min (xi) follows exponential distribution with parameter…

Q: 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y =…

A: A random variable follows a Normal distribution with mean μ and variance σ2 Random Variable Mean…

Q: how that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .

A:

Q: Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of

A:

Q: Let X ~ Beta (2, 2) and Y = 1 / X^2. • Find the cumulative distribution function of Y. • Calculate…

A: Given  X~Beta2, 2 and Y=1X2

Q: If X1=2,X2=3,X3=1,X4=4,X5=1,X6=8 be a random sample taken from a population having variance sigma^2…

A: Given: Data=2,3,1,4,1,6 The sample mean is calculated below: x¯=∑xn=2+3+1+4+1+66=176=2.83 Thus, the…

Q: Suppose X is random variable with E(X^2)= 10 and E(X)=2. What is the variance of X? Suppose X is a…

A:

Q: Let X be a normal random variable with mean μ=10 and variance σ^2=36. Find (a)P{X5} (c)P{4<X<16}

A: Mean()=10Variance()=36standard deviation()==6

Q: A regression model relating x, number of salespersons at a branch office, to`y, annual sales at the…

A: The independent variable is number of sales persons. The dependent variable is annual sales. We have…

Q: If independent random variables 'X' and Y have the variances 36 and 16 respectively, find the…

A:

Q: how to find that which type of kurtosis is represent by the curve in sample distribution.

A: Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from…

Q: Researches are interested in whether or not the average fuel economy for compact cars is the same as…

A: Compact cars: Sample size n1=36 Sample mean x¯=38 Sample variance s12=25 Sample standard deviation…

Q: a)Find the estimator for the method of moments for beta and the numerical value of it?

A: Given: A sample of 20 observations is broken from the normal distribution .

Q: Explain at least two differences between the following two point estimations of the population…

A: Both the given estimators are used to estimate population varaince in different situations.

Q: Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional…

A: The linear regression model is valid when it satisfies few assumptions like Linearity, Normality,…

Q: let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2.…

A: Result: If X~N(0,1) then X2~χ2(1) χ2(n1)+χ2(n2)=χ2(n1+n2)  E(χ2(n))=n and V(χ2(n))=2n

Q: State wh 362 The iegree of treedom of t-test for independent samples (where oy & oz are unknown and…

A: Given data, n1=37 n2=43 Given df=79