3. Let X₁ X₂..... X, be a random sample from a Poisson distribution with mean μ. Derive the limiting distribution of X.
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- 3. Let Y₁ 5)7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
- I want to ask how do we know when we need to use the continuity correction like the second image and when will we use the normal distribution like the 1st image? Thank youDetermine if the following scenarios follow a Poisson distribution or do not follow a Poisson Distribution. • You work in a shoe shop and you want to find the distribution of the total number of people who come into the store in a day. You also observe that there are usually more people who come into the shop over lunchtime (10-2 pm) and more people who come into the store after they finish work (5 pm-6 pm). Let X be the number of people who come into the shoe shop on a given day. No - not Poisson • You love peanut butter and want to know how many people buy peanut butter from Trader Joe's. One summer you have nothing to do so you go and stand in Trader Joe's every day and count how many people buy peanut butter in a given week. You assume that consumers do not impact each other's decisions. Let Y be the number of people who buy peanut butter in a given week. Yes - Poisson You want to know how many people in a group of 100 take painkillers if they have a headache. You think that the…5. Let (Xi, Yi), i 1, 2, ,n, be a random sample from a bivariate normal distribution. Find the joint distribution of (X,Y).
- Let X be a continuous random variable whose distribution is given by X ~ PAR(6.2). Find the 65th percentile, 65. O 1.2461 O 1.0613 O 1.1229 O 1.1845 O 1.3077Let X₁, X₂.....X₁ be a random sample from an exponential distribution with parameter 8. Find the MLE for P(X≥1).Let Zı, Z2, ... Zn represent a random sample of size n from a standard normal distribution. f n= 5; X= Z + Z+ Z and Y=Zi+Zs. What is the distribution of 2X/3Y? (Note: you must either prove or justify your argument using known theorems)
- 5. Assume that X is a discrete random variable with cumulative distribution function (cdf) F(x) given below. F(X) 0-8 0.b t0.2 -2 2 3 ->1 Find Mode and Skewness of x-distribution.6. Let X1, X2, ...X100 denote a random sample of size 100 from an exponential distribution with mean 1. Let Y equal the sum of all the X's. Approximate the probability that Y is greater than 110. |
