University of Melbourne

The Pearson residuals in the higher control category show a mixed relationship between language use and cognitive control. Bilingual residual 0.058, multilingual -1.274. The residuals for lower and medium control also deviate from the expected further indicating a complex relationship between language and cognitive control. Why?

please write more succinctly This data provides insights into how language proficiency may influence cognitive control levels. The findings suggest a potential association between language use and cognitive control. This is indicated by the varying counts and Pearson residuals across different language groups and cognitive levels. As presented by Figure 1, the Pearson residuals in the higher control category show bilingual 0.058 and multilingual -1.274 indicating a mixed relationship between language use and cognitive control. The residuals for lower and medium control additionally show a deviation from the expected frequencies. Thus, the Pearson residuals give an indication into the nature of the relationship between language use and cognitive control. Our hypothesis is supported by the data obtained showing multilinguals have higher cognitive control than expected by chance.

Suppose that X has an exponential distribution with parameter λ > 0. For x ∈ R let ceilx denote the smallest integer that is greater than or equal to x. The distribution of Y = ceilX. Let Z = X · Y. Show that E[Z] = [e^−λ - (e^−λ)/λ + 1/λ]/(1 − e^−λ)^2 .

Suppose that X has an exponential distribution with parameter λ > 0. For x ∈ R let ceilx denote the smallest integer that is greater than or equal to x. The distribution of Y = ceilX. Let Z = X · Y . Find the density function of Z

Suppose that X has an exponential distribution with parameter λ > 0. For x ∈ R let ceilx denote the smallest integer that is greater than or equal to x. The distribution of Y = ceilX. Let Z = X · Y .For z ∈ R, find the tail probability P(Z > z).

Suppose that X has an exponential distribution with parameter λ > 0. For x ∈ R let ceilx denote the smallest integer that is greater than or equal to x. The distribution of Y = ceilX. Let Z = X · Y . Describe the subset S_Z of R+ where Z has positive density. Hint: start by considering the case where X ∈ (n − 1, n] for n ∈ N. You should be able to express S_Z as a union of disjoint intervals.