Homework 1Question 1 (10pts)a) What is probability of observing 61325 when rolling fair dice?Probabilities for fair dice: P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6b) What is probability of observing 61325 when rolling loaded dice?Probabilities for fair dice: P(1)=P(2)=P(3)=P(4)=P(5)= 0.1 and P(6)=0.5Question 2 (50pts). On a hypothetical island virus outbreak becomes a threat of future pandemic. Researchers have narrowed down the cause of outbreak to two viruses (virus 1 and virus 2). The DNA sequencing lab receives a sample for further analysis. Unfortunately, the sample was contaminated and the removal of foreign DNA leaves the lab with a short DNA fragment: AGTAGCTTCCAG. Given all available information (provided below) how can lab determine the type of the virus that caused the outbreak.Nucleotide probabilities of virus1P(A)=P(T) =0.3P(G)=P(C) = 0.2Nucleotide probabilities of virus 2P(A)=P(T)=P(G)=P(C)= .25Assume:- Virus 1 and Virus 2 are equally likely to occur in nature.- nucleotides are independent and identically distributed.Question 3 (40 pts)Align two sequences shown below using Needelman Wunsch algorithm.Use match score of 4, mismatch score of -4 and gap penalty score of -2.Show:a) dynamic programming matrix with scores (as it shown in Figure 6.1, Ewens or in Figure 2.5, Durbin which is available under Course Content.)b) trace back pointersc) alignment scoresequences:sequence 1:AGAGCTCACAAsequence 2:AGTAGCTTCCAAA

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Statistical Bioinformatics .

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