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  1. J

    is there interaction effect in RCBD with a single observation per cell ?

    The statistical model for a Randomized Complete Block Design (RCBD) with a single observation per cell is: y_{ij}=\mu+\tau_{i}+\beta_{j}+\epsilon_{ij};\quad i=1,\ldots ,a, \quad j=1,\ldots, b, where y_{ij} is a random variable that represents the response obtained on the ith treatment of the...
  2. J

    Statistical model for *Complete Randomized design (CRD)*

    Consider the statistical model for *Complete Randomized design (CRD)* y_{ij} = \mu + \tau_i + \epsilon_{ij}, \quad i=1,\ldots ,k, \quad j=1,\ldots, n_i, where $y_{ij}$ is a random variable that represents the response obtained on the $j$th observation of the ith treatment, and \epsilon_{ij}...
  3. J

    How can i comment on the following graphs of Binomial distribution.

    I am using 'R' to draw the graph : par(mfrow=c(2,2)) graph(10,0.05) graph(20,0.05) graph(50,0.05) graph(200,0.05) How can i comment on the graphs? Does it " as number of trials increases, probability of getting the zero success decreases" ?
  4. J

    graph of binomial distribution in R.

    I want to draw the density of Binomial distribution in R. I tried as : x=dbinom(1:10,10,0.5) x barplot(x) I want to write 1 under the 1st bar, 2 under the 2nd bar, 3 under the 3rd bar and so on. I actually want to draw a graph same as...
  5. J

    R, When does the error "$ operator is invalid for atomic vectors" occur?

    pmf <- array(c(2/15,1/15,4/15,1/15,3/15,4/15),dim=c(2,3), dimnames=list(X=1:2,Y=1:3)) pmf$Y Error in pmf$Y : $ operator is invalid for atomic vectors please give detail explanation. I have faced the problem a number of times not only for 'array' but also for 'data.frame'.
  6. J

    How to read the data `veteran` from package `survival` in r?

    `state.x77` is a `R` built-in data set.To read the data `state.x77` , i only write `state.x77` in the `R console` and the data set comes immediately. Now i have to read the data `veteran` from package `survival`. But if i write veteran Error:object veteran not found. How...
  7. J

    plot histogram in r

    I have the following data set: \begin{tabular}{|l c r|} \hline X & Y & Type \\ \hline 32 & 48.5 & A \\ 36.3 & 42.9 & A \\ 45.8 & 75.8 & A \\ 60.5 & 5457.6 & B \\ 12 & 6666 & B \\ 24.2 & 48.5 & C \\ 271 & 2796.6 & C \\ \hline \end{tabular} Now I have to draw histogram of the...
  8. J

    R homework

    1. Fit appropriate regression models to describe relationship between the variables X and Y using the following three data sets separately. Use Y as the response and X as the explanatory variable. You must show all the necessary tables and fi gures for the model fi t and also comment on the fi...
  9. J

    r program. Draw the histogram of the eruption waiting periods in 'faithful '.

    #head(faithful) vct <- faithful$waiting #vct #is.vector(vct) range(vct) cls.boundary <- seq(40,100,by=10) #cls.boundary cut.vct <- cut(vct,cls.boundary,right=FALSE) #str(cut.vct) freq<-table(cut.vct) show<-cbind(freq) #show hist(show) Is this right? The Y-axis(frequency) of the...
  10. J

    non-central chi-square distribution.

    If X_i is distributed as normal with mean \mu and variance-covariance matrix D,where D is the diagonal matrix, then show that X^TD^{-1}D is distributed as noncentral \chi^2 with k degrees of freedom and noncentrality parameter \mu^TD^{-1}\mu=\lambda.
  11. J

    What will be the transformation and Jacobian of transformation for the following case

    Let X_i\sim N(\mu_i,\sigma^2) ; where [i=1,2,\ldots,n] show that \bar X and (X_i-\bar X) are independent. If all X_i had same mean \mu then we transform the random variables X_i; [i=1,2,\ldots,n] to Y_1=\bar X Y_2 =X_2-\bar X Y_3 = X_3-\bar X \vdots Y_n = X_n-\bar X...
  12. J

    Checking the Independence.

    Let X_i\sim N(\mu,\sigma^2) ; where [i=1,2,\ldots,n] Z_i\sim N(0,1) ; where [i=1,2,\ldots,n] Proof that \frac{(\bar X-\mu)}{\sigma} and \sum_{i=1}^n\frac{(X_i-\bar X)^2}{\sigma^2} are independent, which implies \bar X and \sum_{i=1}^n(X_i-\bar X)^2 are independent. If i show that \bar...
  13. J

    Cumulants of non central chi-square distribution

    Cumulant generating function is defined by logarithm of Moment generating function. K_X(t)=\log M_X(t) let X is a non central \chi^2 variate with parameters degrees of freedom,n and non-centrality parameter,\lambda. Moment generating function of X is...
  14. J

    An Exercise of noncentral [math]\chi^2[\math] distribution.

    An Exercise of noncentral chi-square distribution. Let Y_1,\ldots,Y_n be independent random variables with Y_k distributed as N\sim(a_k,\sigma^2) , and \bar Y=\sum_{k=1}^{n}\frac{Y_k}{n} denote the sample mean, S^2 denotes the sample variance. Then show that...
  15. J

    How can i compute the following situation in R?

    Suppose that an urn contains a number of black and a number of white balls, and suppose that it is known that the ratio of the numbers is $\frac{3}{1}$ but that it is not known whether the black or the white balls are more numerous. Find the estimator of the probability of drawing a black ball...