Consider a branching process with offspring distribution {βk}k≥0 and assume 0 < β0 < 1. Suppose the evolution is altered as follows. Start with X0 = 1, a single individual. If the next generation is not empty (that is, if X1 > 0), they invite an immigrant to join them (that is, X1 is replaced by X1 + 1). After that the evolution continues according to the usual rule. In particular, no further immigration takes place. Find the extinction probability ˆπ of this new process, expressed in terms of β0 and the original extinction probability π. For which values of π do we have ˆπ < π, in other words, the immigrant strictly improves the chances of survival? Hint: Condition on the number of offspring of the first individual.

a researcher conducts an experiment on the secretion of a particular hormone in mice. scientists inject mice with a substance that stimulates the production of the hormone. the scientists then test the levels of hormones produced by the mice. the tool used to measure the hormones consistently detects the levels at 10 points lower than the actual hormone levels in the mice. this tool makes measurements, but the measurements aren't .

explanation:

no u

evidence and logical support is essential for a scientist to do in order to maintain credibility. this is because no one can believe without any logic and without any evidence.hence a scientist can maintain credibility by proving himself and by answering logically so experiments prove very beneficial. logical hypothesis give conclusion which is acceptable. therefore, there are two main factors to maintain credibility by a scientist is evidence and logical support.