over 1,2. .10 a p.m.f.? For which value of the parameter a is the functionf(x)000 *...
Obtain the value of "c" for which the followeing function f(x) would be a p.m.f. of a discvrete random variable X:- f(x) = c(x-1), x=1,2,...,10 0, elsewhere (1) Determine expectation and variance of X. (2) Find third order central moment of X (3) Find the moment measures of skewness for the distribution.
Consider a pair of independent random variables X and Y with identical marginal p.m.F.'s (1-0) for z E 10, 1,2,... otherwise {(1-0 gu otherwise 1,2,..) pr(v) (This is an alternative way of defining the geometric distribution.) Complete the derivation of the distribution of Z X +Y below. (1-0) Complete the derivation of the conditional distribution of XZ If we know that X and Zz,then If we know that Zthen X can take any value between below and Complete the derivation...
3. Find the first derivative of a functionf(x)-ex (a) Use calculus to determine the correct value of the derivative at x = 2. If h = 0.25, (b) Evaluate the second-order centered finite-difference approximation (e) Evaluate the second-order forward difference approximation. (d) Evaluate the second-order backward difference approximation. (e) Create a MATLAB function program, which gives output up to second order centered finite difference approximation of second derivative "(xo). The input arguments aref n (order of approximation, 1 or 2),...
Fill out the table and determine the value of the following quantities, Using the following p.m.f. f(x)= (x+1)2/91, x=0,1,2,3,4,5 i.Probability Table: x f(x) xf(x) 0 1 2 3 4 5 ii . What is the E[X]? iii. What is the E[x2]? iv. What is Var(x)?
Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be a Bernoulli random variable with parameter 1/2 such that X, Y are independent. (1) Find the PMF of the random variable Z, where Z XY. (2) Compute the third moment of Z, that is, E[z2
3) Suppose F(x) is an antiderivative of f(x). Use the graph of the functionf(x) below to answer the following: flx) a) Approximate f'(6), and explain/show how you arrived at your answer 6 4 3 2 b) Explain/show why F'(6) 2 1 2 3 4 5 6 7 c) Approximate o f(x)dx, and explain/show how you arrived at your answer. d) Explain/show why f'(x)dx-3.
11.3) Bayesian Parameter Estimation. Suppose Λ is a random parameter with prior given by the Gamma density 7(a) = CM2-1/4 2 0}, where a is a known positive real number, and I is the Gamma function defined by the integral ['(x) = ( +12'dt, for x > 0 Jo Our observation Yis Poisson with rate A, i.e., p(y) = P({Y = y}|{A =2}) = - - ale-2 - y = 0, 1,2,.... O y! (a) Find the MAP estimate of...
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x) =((n|x)(p^x)(1−p)^(n−x))/(1−(1−p)^n), if x= 1,2,3,···,n. •Find the moment generating function (m.g.f.) and the probability generating function(p.g.f.). •From the m.g.f./p.g.f., and/ or otherwise, obtain the mean and variance. Show all the necessary steps for full credit.
DI Question 6 2 pts Consider the following Truth table 000 0| 0 000 11 00 10| 0 00 1 11 0100|1 01 0 11 0 01 1 0 | 0 01 1 1| 0 100 0 | 0 100 1| 1 10 1010 10 1 1| 1 11 001 O 11 0 1 1 0 Fill the following K-map 01 2 Select ▼ | [Select] 01 sect] | ▼ | [Select] ▼ | [Select] [Select] f11 15 | ▼...
(5) Recall that X ~Uniform(10, 1,2,... ,n - 1)) if if k E (0, 1,2,... ,n -1, P(x k)0 otherwise (a) Determine the MGF of such a random variable. (b) Let X1, X2, X3 be independent random variables with X1 Uniform(10,1)) X2 ~Uniform(f0, 1,2]) Xs~ Uniform(10, 1,2,3,4]). X3 ~ U x2 ~ Uniform(10, 1,2)) 13Uniform Find the laws of both Y1 X1 +2X2 +6X3 and Y2 15X1 +5X2 + X3. (c) What is the correlation coefficient of Yi and ½?...