Develop a random variate generator for a random variable X with the pdf if x < 0, f(x) = %3D e-2x if x 2 0.
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- Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the expression of the correlation of X and XY in terms of mu and sigma.Expression levels of GeneA and GeneB were measured in 10 cell lines. The researcher would like to know if expression levels of GeneA and GeneB are related.Use a non-parametric method to test if GeneA and GeneB are correlated.For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish
- Installation of some software package requires downloading 82 files. On the average, it takes 15 sec to download one file, with a variance of 16 sec^2. What is the probability that the software is installed in less than 20 minutes?Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator ofDefine interpretation of Least Squares Regression Variance of α^ & β^
- The number of offspring of an organism is a discrete random variable withmean μ and variance σ^2. Each of its offspring reproduces in the same manner. Find the expected number of offspring in the third generation and its variance.Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output: Estimate SE Pr(>|Z]) (Intercept) to_multiple -0.8166 0.0883 -9.248 -2.6583 0.3023 -8.7936 winner 1.5705 0.3178 4.9418 format -0.0799 0.1232 -0.6485 0.5166 re_subj -2.807 0.3652 -7.6862 (a) Write down the model using the coefficients from the model fit. log_odds(spam) = to_multiple + winner + format + re_subj (b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?p^2 +2pq +q^2 with A=p frequency a=q frequency Aa x Aa heterozygous cross Assume there is a heterozygous survival advantage, where an AA type egg has probability 0.8 of mating and an aa type egg has probability 0.2 of mating, but Aa type eggs have 1.0 probability of mating. Explain why the new ‘total’ frequency of all chromosomes in reproducing adults (i.e., in the next generation born) will not be 100% but instead will be F(p) = 0.8p^2+ 1.0 ∙2pq + 0.2q^2 This is called the balance equation. Find p1, the frequency of A in the adult population, if an AA type egg has probability 0.8 of mating and an aa type egg has probability 0.2 of mating, but Aa type eggs have 1.0 probability of mating. Remember that the frequency is the proportion out of the total and use the balance equation you derived above. Note I think finding p1 involves implicit differentiation. Frequency of A is described as variable p.
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