The penetrance function is the name given to Pr(Y|G), that is, the probability of observing the phenotype Y given the genotype G. For Mendel's pea plant experiments we can compute the penetrance function. (a) For the white/purple flower experiment, let Y = 1 be the phenotype of purple colored flowers and Y = 0 denote the phenotype of white colored flowers. In this setting compute i. Pr(Y= 1|G= Rr) = ii. Pr(Y= 1|G = RR) = iii. Pr(Y = 1|G = rr) = iv. Pr(Y=0|G= Rr) = v. Pr(Y=0|G = RR) = vi. Pr(Y=0|G = rr) = = (b) If a genotype (dd, dD, or DD) of interest has no effect on the phenotype of interest, what's the relationship between Pr(YG = dd), Pr(Y|G = Dd), and Pr(Y|G = DD)? (c) In the above example with flower color Y was a qualitative phenotype (e.g. white flower or purple flower). If Y is not qualitative we can still talk about the pen- etrance function but we need to use a distribution. For example, if Y is quanti- tative, (e.g. the height of a plant) we may give the penetrance function as the normal probability density function. That is, 1 Pr(Y|G) = f(YUG,0) = exp{(Y-MG)/20), 270 (1) where pc is the mean of distribution and depends on the genotype G. Suppose that we have a quantitative trait, which is distributed as N(,1) when there are two different allele variants (e.g. Rr) and N(0, 1) otherwise. Calculate the probability that a randomly selected heterozygous person with two different allele variants has a trait higher than a homozygous person (i.e. a person having both variants or no variants) when = 2.