Question

Help me the part b please, if possible part c too

The binomial distribution is B(n,pl-probability for variable X to be equal to K P(X-k) with m we define-np, which is the probability of success for n events each with probability p we take the limit when う00 (we consider a very large number of events M-1 2 Mass (Da) 2. Poisson distribution a. Show that the Poisson distribution,p(kl)arises from the binomial distribution in the limit that p 1 and the number of trials N >> 1 . what is λ? b.) Find the variance ơ2 of the distribution c.) The rates of human genomic mutation are about 2x10-8 per base per generation. How many mutations would you expect on average in a given gene per generation. What is the probability of one or more mutations in a given typical gene (of 1000 bp) in 10 generations?

Answer 1

We know that f (x) any e^lambda = 1 + lambda + lambda^2/2! + = sigma^infinity_x = 0 lambda^x/x! sigma^infinity_x = 0 lambda^x/x ! e^-lambda = 1 we define f (x) = e^-lambda lambda/x! x = 0, 1,2, else where then f (x) greaterthan 0 forall x and sigma_x f (x) = sigma^infinity_x = 0 e^- lambda s lambda^x/x ! = 1 this show f (x) is a pdf distance type such pdf is called passion pdf 8 the random variables x having pdf of this form is called poison variable or to have is called distribution with parameter Now we have to find variable(sigma^2) of this distribution the mgf of points distribution is given b y \r\n M (t) = E (e^tx) = sigma_x e^tx f (x) = sigma^infinity_x = 0 e^tx - e^lambda lambda^x/x! = e^lambda sigma^infinity_x = 0 (lambda e^t)/ x ! = e^-lambda e^lambda et