8. Consider the class of hypergeometric probability distributions PD D 0, 1,2.. ,N), where N)-i(D) (N-D),...
Consider a hypergeometric probability distribution with n = 4, R = 4, and N=8. a) Calculate P(x = 0). b) Calculate P(x>1). c) Calculate P( x 4 ). d) Calculate the mean and standard deviation of this distribution a) P(x = 0) = (Round to four decimal places as needed.) Notes Need all parts answered please
Please answer a,b,c,d Consider a hypergeometric probability distribution with n=3, R=5, and N = 10. a) Calculate P(x = 0). b) Calculate P(x > 1). c) Calculate P(x<3). d) Calculate the mean and standard deviation of this distribution. a) P(x = 0) = (Round to four decimal places as needed.)
i) CHOOSE which of these probability distributions is most appropriate to describe a random variable X defined as "the number of approved state-government construction contracts bid by the engineering firm in the recent year". * X~Poisson(8) X~Po(3.2) X~Binomial(8,0.4) X~Negative Binomial(8,0.4) X~Geometric(0.4)ii) Using the random variable X in question 1(i), which of the following mathematical expressions indicates: the probability that the engineering firm will not get any state-government construction contracts that they have bid in the recent year? * P(X=8) P(X...
Consider a DTMC X;n 2 0 with state space E 0,1,2,... ,N), and transition probability matrix P = (pij). Define T = min(n > 0 : Xn-0), and vi(n) = P(T > n|X0 = i). Use the first-step analysis to show that vi (72), t"2(n), . . . , UN(n)) = where B is a submatrix of P obtained by deleting the row and column corresponding to the state 0. Hint: First establish a recursive formula v(n )-ΣΝ1pijuj(n-1). Consider a...
4. (20 pts) Consider the following regression model, i = 1,2. ,...n, N (0, 2/i) where , 1,2,...,n are independent, but c; ~ (a) Do you think if it is suitable for the (ordinary) least square regression technique to apply the data (x4, Y;)? Give a brief reasoning (b) Construct a transformed model so that you can use the ordinary least square method (c) Find the parameter estimates for the transformed model in (b) WIS (d) Find the weighted least...
Problem 2. Consider a random walk on the n cycle {1,2,...,n} that moves anticlockwise with probability 1/2 and clockwise with probability 1/2. Define the function n-k f(x)k に1,2, . . . , n. show that f is harmonic on the set D = {2,3, , n-1). Problem 2. Consider a random walk on the n cycle {1,2,...,n} that moves anticlockwise with probability 1/2 and clockwise with probability 1/2. Define the function n-k f(x)k に1,2, . . . , n. show...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Let X(n), n 0 be the two-state Markov chain on states (0,1) with transition probability matrix probability matrix 「1-5 Find: (a) P(x(1) = olX (0-0, X(2) = 0) (b) P(x(1)メx(2)). Note. (b) is an unconditional joint probability so you will nced t nclude the initi P(X(0-0)-To(0) and P(X(0-1)-n(0).
1. Consider the Probability distributions shown in Figure below, where the signal voltage for binary 1 is V1 and Vih-V12 1 level o(n Threshold vohage 0 level Additive noiac,y P(y|の a) If σ-0.20 y for p(y/0) and σ-0.24 Vi for p(y/1), find the error probabilities Po(Vh) and Pi(Vth) b) If a-0.65 and b-0.35, find Pe c) If a-b-0.5, find Pe
Let A-(Aij)i iJSn є {0,1)"xn denote the symmetric adjacency matrix of an undi- rected graph. For iメj, we have Aij = 1 if entity i and j are connected in a network and 0 otherwise: A 0, i-1,..., n. The stochastic block model (SBM) postulates where is a full rank symmetric K x K connectivity matrix with entries in [0, 1]. a) Consider the matrix P-M MT, where M {0,1)"xK denotes the community k-1,... , K. Show that under (1),...