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- 2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ? 2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction? 2c) Using the previous results for lambda and continuity correction, find z, then graph and use your table to find φ table value of z Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.Suppose that X has a Poisson distribution with h = 80. Find theprobability P(x is less than or equal to 80)
- Let X1 and X2 be observations of a random sample of size n = 2 from a Cauchy Distribution.Find P(X1 < −1 and 1 < X2)Let X1, X2, ... Xn random variables be independent random variables with a Poisson distribution whose parameters are l1, l2, ... ln, respectively. Which of the following is the moment generating function of the random variable Z defined as (the little image)?If X has an F distribution with ν1 and ν2 degrees offreedom, show that Y = 1Xhas an F distribution with ν2 and ν1 degrees of freedom.
- Suppose x has a distribution with μ = 11 and σ = 3.A button hyperlink to the SALT program that reads: Use SALT.(a) If a random sample of size n = 32 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σx to two decimal places and the probability to four decimal places.)μx = σ x = P(11 ≤ x ≤ 13) = (b) If a random sample of size n = 62 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σ x to two decimal places and the probability to four decimal places.)μx = σ x = P(11 ≤ x ≤ 13) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)The standard deviation of part (b) is ---Select---part (a) because of the ---Select---sample size. Therefore, the distribution about μx is ---Select---In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Poisson distribution with probability mass function f(x), where f(x) = θ x e −θ/x! and θ is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was.Suppose x has a distribution with μ = 10 and σ = 2.A button hyperlink to the SALT program that reads: Use SALT.(a) If a random sample of size n = 44 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)μx = σ x = P(10 ≤ x ≤ 12) = (b) If a random sample of size n = 66 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σ x to two decimal places and the probability to four decimal places.)μx = σ x = P(10 ≤ x ≤ 12) =
- Let X1, X2, X3 and X4 be exponential(1) random variables. Find the joint distribution of X1/(X1+X2+X3+X4) and (X1+X2)/(X1+X2+X3+X4) and (X1+X2+X3)/(X1+X2+X3+X4) using Jacobian method?Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4 explain.The number of passengers willing to travel with a certain train is as- sumed to be a Poisson variabel with parameter µ = 300. How many seats should the train have if the probability for an over-booked train should be at most 1%?