If X is a negative binomial rv, then Y= r+X is the total number of trials necessary to obtain r S’s. Obtain the mgf of Y and then its mean value and variance. Are the mean and variance intuitively consistent with the expressions for E(X) and V(X)? Explain

Q: If the variances for independent random variables X and Y is Var(X)=0.15 and Var(Y)=5.62 then Var…

A: Given that  Var(X)=0.15 Var(Y)=5.62

Q: (i) Verify that P(|38| ≤e) = 1-a and conclude that, if o is known, [B Xi: Yi: Xi: Yi: O √nvx is a…

A: Given that β^~Nβ, σ2nvx, where vx is the variance of the empirical distribution of x1, x2,..., xn.…

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A: We have given that  X 10 5 P(X) 0.4 0.6

Q: e simple regression line y=α+βx for th

A: given x and y to find = simple regression line y=α+βx

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A: It was stated that the results of Levene's test are: Upper critical value : F(2,96)=1.85 The…

Q: 3 For an SRS {Y: ³;=, from the normal distribution 1 fiy (цілето 2) vivore (y;u, - Show that the…

A: Here, The simple random samples of size n taken from the normal population. We have to show that the…

Q: Which of the following statements is FALSE? O When combining forecasts using the OLS method, it is…

A: Which of the following is false? When combining forecasts using the OLS method, it is possible for…

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A: Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a…

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A: Given that, The random variable P is the number of points that occur. E[P]=121Var[P]=230 The amount…

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A: Given,n=20r=0.40SSY=100

Q: Let X N(μ, o²). Find the MSE of the (uncorrected) sample variance 152 as an estimator for o² and…

A:

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A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: a) What is dependent and independent variables? b) Fully write out the regression equation. c) Fill…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a…

A:

Q: Let x represent the number of mountain climbers killed each year. The long-term variance of x is…

A: Given information s2 = 110.6, α = 0.01, n = 8 years a) Level of significance α = 0.01 Null and…

Q: If X is a normal variate with mean 5 and variance 4. Find P ( -1.5 < X < 2)?

A: Given,mean(μ)=5standard deviation(σ)=2

Q: 1.Consider the following two simple regression models : Model I : Y, = B, + B,X; + µ, Model II : Y,…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: A regression and correlation analysis resulted in the following information regarding a dependent…

A: Solution Given Σx  =  90 Σy  =  170 n  =  10 SSE  =  509.98   Σ(y − y)(x − x)  =  467…

Q: current variance is less than 5.1. (a) What is the level of significance? State the null and…

A: It is given that  Sample size n = 51 Sample variance s2 = 3.1 Level of significance = 5% Note :…

Q: if X is a normal random variable with mean u = 3 and variance 62 = 16, find P(X >3), P(X>-1)

A: Mean=3, variance=16

Q: Two zero-mean random variables X and Y have variances o =9 and o = 4. The %3D correlation…

A:

Q: Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941,…

A: n= 41 Sample size  s2=2.9 Sample variance σ2=5.1  Population variance

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A:

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A: Null and alternative hypotheses: Let σ12 and σ22 be the variance in the aerobic capacity of smokers…

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A:

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A: GIVEN : Let X(0) , X(1) , X(2),....X(N-1) are independent and normally distributed with mean zero…

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A: Introduction: Consider a multiple regression model with response variable, y, and two explanatory…

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A:

Q: If X is a Poisson variate such that 4) + 90 P(X=6), find the P(X=2)=9P variance (X =

A:

Q: 5. Consider the equation Y = Bo + B₁X₁ + B₂X2, where X₁ (μx₁,₁) is independent of X₂ ~ (x₂,₂). With…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be…

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Q: m variable X be the height of a randor 2 from the same group in millimeters, positive a, b e R there…

A: True

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A: Given the variance of the forecasted error using the Exponential Smoothing (ES) method as

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A: Givenn=6∑x=28∑y=73∑xy=404∑x2=162∑y2=1075

Q: Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5.…

A: Given Data: Var(X)=2 Var(Y)=5

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A: Given information:n= 50 observation k= 1 independent variables

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A: Given Data: Mean=50 Variance=100   X~ Normal (50, 102)

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A: Formula used: The standard deviations of sampling distribution is=  Sd/ √n

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A:

Q: Compute the residual

A: here given regression line y = 24+5x   residual = actual value - predicted value

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.