2. A discrete random variable X has the following pmf: p(x)| 1-8 30/4 θ/4 A random...
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...
Let X be a discrete random variable with the following PMF. Px(k) = 1/4 for k = -2 1/8 for k = -1 1/8 for k = 0 1/4 for k = 1 1/4 for k = 2 0 otherwise Define a new random variable Y = (X + 1)2 a) Find E[X] and Var[X] b) Find the range of Y and write its PMF. c) Show that the PMF of Y is a valid PMF. d) Find P(Y ≤...
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...
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
Let X be a discrete random variable with a the PMF such that P(X =x)= 2/3^x for x =1, 2,3,....... Find the expected value Of X.
Let X be a discrete random variable with pmf p(n) = (n−1)(0.4)2(0.6)n−2, n ≥ 2 and 0 otherwise. Find the mode of X
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)