Can you explain how to do parts a-c?
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Can you explain how to do parts a-c?
4. Suppose that X is a discrete random...
2. A discrete random variable X has the following pmf A random sample of size n...
2. A discrete random variable X has the following pmf A random sample of size n 30 produced the following observations: (a)) Find and s for this sample Find E(X) and var(X) (iii) Find the method of moments estimate of θ (iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the maximum likelihood estimate of θ is -1 fo/n, where fo is the number of observed 0's in the sample. (iii) Find...
NOTE: DO PART b) ONLY 2. A discrete random variable X has the following pmf: A...
NOTE: DO PART b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
NOTE: DO Part b) ONLY 2. A discrete random variable X has the following pmf: A...
NOTE: DO Part b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
2 Suppose that we observe the continuous random variable X (X1,.., Xn) with state space S,...
2 Suppose that we observe the continuous random variable X (X1,.., Xn) with state space S, whose distribution we do not know but we are assuming that its p.d.f. belongs to a known family of distributions {fe;Be Θ). We construct an estimator for the unknown parameter θ(X) (a) Explain why it is wrong to write E(ex) and correct it. 12 marks (b) Explain the difference between pdf and likelihood function. [1 mark] (c) Explain the different between estimate and estimator....
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; =...
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; = 1) = 01, P(Y; = 2) = 62, where the parameter vector 6 = (60,61,62) satisfies: 0; > 0 and 200; = 1. (a) Calculate E[Y] and EY?), and use the results to derive a method of moments estimator for the parameters (01,02). (b) Show that the maximum likelihood estimator for 6 = 60, 61, 62) is - Ôno = ôz = = 1(Y;=0),...
3. Suppose Xi, X2, and X are independent random variables drawn from a binomial distribution with parameters p and n. The observed values are Xi -3, X2-4, and (a) Suppose n 12 and p is unknown. What...
3. Suppose Xi, X2, and X are independent random variables drawn from a binomial distribution with parameters p and n. The observed values are Xi -3, X2-4, and (a) Suppose n 12 and p is unknown. What is the maximum likelihood estimator (b) Suppose p - 0.4 and n is unknown. What is the maximum likelihood estimator for p? for n? (Note: Since n is discrete you can't use calculus for this; just write the formula and use trial and...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
Given probability Density Function pox)- (0+1)x and data D randomly drawn independently from D with pdf...
Given probability Density Function pox)- (0+1)x and data D randomly drawn independently from D with pdf p(x), estimate the parameter 0 using maximum likelihood estimation. Hint: Probability P(D) I1-1Px) , log likelihood function 1(O) should be maximized to determine θ. 2. (xl,x2,.. .Xa) samples [10]
Random variable X corresponds to the daily number of accidents in a small town during the...
Random variable X corresponds to the daily number of accidents in a small town during the first week of January. From the previous experience (prior infor- mation), local police Chief Smith tends to believe that the mean daily number of accidents is 2 and the variance is also 2. We also observe for the current year the sample number of accidents for 5 days in a row: 5,2,1,3,3. Let us assume that X has Poisson distribution with parameter θ ....
Need help with this Problem 4 A discrete random variable X follows the geometric distribution with...
Need help with this
Problem 4 A discrete random variable X follows the geometric distribution with parameter p, written X ~Geom(p), if its distribution function is fx(x) = p(1-p)"-1, xe(1, 2, 3, . . .} The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that Ix(z) is indeed a probability inass function, i.e., the sum over all possible values of z is one...
2. A discrete random variable X has the following pmf A random sample of size n 30 produced the following observations: (a)) Find and s for this sample Find E(X) and var(X) (iii) Find the method of moments estimate of θ (iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the maximum likelihood estimate of θ is -1 fo/n, where fo is the number of observed 0's in the sample. (iii) Find...
NOTE: DO PART b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
NOTE: DO Part b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
2 Suppose that we observe the continuous random variable X (X1,.., Xn) with state space S, whose distribution we do not know but we are assuming that its p.d.f. belongs to a known family of distributions {fe;Be Θ). We construct an estimator for the unknown parameter θ(X) (a) Explain why it is wrong to write E(ex) and correct it. 12 marks (b) Explain the difference between pdf and likelihood function. [1 mark] (c) Explain the different between estimate and estimator....
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; = 1) = 01, P(Y; = 2) = 62, where the parameter vector 6 = (60,61,62) satisfies: 0; > 0 and 200; = 1. (a) Calculate E[Y] and EY?), and use the results to derive a method of moments estimator for the parameters (01,02). (b) Show that the maximum likelihood estimator for 6 = 60, 61, 62) is - Ôno = ôz = = 1(Y;=0),...
3. Suppose Xi, X2, and X are independent random variables drawn from a binomial distribution with parameters p and n. The observed values are Xi -3, X2-4, and (a) Suppose n 12 and p is unknown. What is the maximum likelihood estimator (b) Suppose p - 0.4 and n is unknown. What is the maximum likelihood estimator for p? for n? (Note: Since n is discrete you can't use calculus for this; just write the formula and use trial and...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
Given probability Density Function pox)- (0+1)x and data D randomly drawn independently from D with pdf p(x), estimate the parameter 0 using maximum likelihood estimation. Hint: Probability P(D) I1-1Px) , log likelihood function 1(O) should be maximized to determine θ. 2. (xl,x2,.. .Xa) samples [10]
Need help with this
Problem 4 A discrete random variable X follows the geometric distribution with parameter p, written X ~Geom(p), if its distribution function is fx(x) = p(1-p)"-1, xe(1, 2, 3, . . .} The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that Ix(z) is indeed a probability inass function, i.e., the sum over all possible values of z is one...
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