(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

According to genetic linkage theory, observed frequencies of four phenotypes

resulting from crossing tomato plants are in the ratio 9/16 + a : 3/16 - a : 3/16 - a : 1/16 + a.

In 1931, J.W. MacArthur reported the following frequencies:

Observed

Phenotype frequency

Tall, cut-leaf 926

Tall, potato-leaf 288

Dwarf, cut-leaf 293

Dwarf, potato-leaf 104

Total 1611

Write down the likelihood of a given these observations. Find the maximum likeli-

hood estimate of a, use it to calculate expected frequencies for the four phenotypes

and compare them with the observed frequencies. Does genetic linkage theory look

plausible?

2. Relevant equations

likelihood of a data set (x_{1}...x_{n}) occuring is the product of f_{X}(x), if X_{i}are independent. Then I could find max likelihood etc as usual

3. The attempt at a solution

Basically I just cannot start this problem at all. I have only ever found likelihood before as a function producing one value, here I seem to want to find the probability that the ratio is b:c:d:e which I have no idea how to do. Also surely I need to know something about the variance of a? At least then I could write down a probability to do with each bit of the ratio?

Sorry if I'm not making much sense/if this is obvious but I have spent a long time attempting this with no luck. Google hasn't helped at all either..

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# Homework Help: Stats question- likelihood function for a ratio

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