Question

Agrobacterium tumefaciens is a bacteria that infects a plant by transferring its own DNA (called transfer-DNA, or tDNA) into the plant genome. This natural mechanism is used as a tool for inserting any given DNA fragment into a plant genome. The insertion location is at random and approximately uniform along the genome. An institute is carrying out insertion-mutagenesis by tDNA on the plant Arabidopsis extensively. They repeated the experiment 100 thousand times and got 100 thousand mutant Arabidopsis plants. The Arabidopsis genome is about 120 million base-pair long. A researcher is studying a given gene (called G) of Arabidopsis and would like to get from the institute a few plants having an insertion in gene G. This gene is 6000 base pair long.

a. What is the probability that a tDNA mutagenesis experiment will produce a plant with insertion in gene G?

b. Let Y be the number of plants produced by the institute and for which the insertion is located in gene G. What is the distribution of Y, what is its expectation E(Y) and what is its standard deviation?

c. What is the probability that the institute can provide the researcher with 2 or more plants?

Answer 1

a) The probability that a tDNA mutagenesis experiment will produce a plant with insertion in gene G =The probabiltiy that the positions among 6000 base-pairs of gene G are chosen among the 120 million base-pair=6000/(120 million)

b) There were 100 thousand experiments done, hence Y~BIn(100 thousand, 6000/(120 million base-pair) , since insertion location is approximately uniform. Hence, E(Y)=(100 thousand)*(6000/(120 million )), sd(Y)=

c)