Assume the following joint probability distribution function where X1 and X2 are random variables denoting faulty components coming from supplier 1 and supplier 2

Assume the following joint probability distribution function where X₁ and X₂ are random variables denoting faulty components coming from supplier 1 and supplier 2, respectively, where a is a constant value.

		X₁
		0	1	2	3
X₂	0	0.15	0.1	0.1	0.1
	1	a	0.15	0.1	0
	2	0	0	0.1	0.1
	3	0	0	0	0.1

The correlation between X₁ and X₂ is:

Expert Solution

The correlation between X₁ and X₂ is 0.414

orchestra answered 3 years ago

X1 and X2 are two discrete random variables. The joint probability mass function of X1 and...

X1 and X2 are two discrete random variables. The joint probability mass function of X1 and X2, p(x1,x2) = P(X1 = 1,X2 = x2), is given by p(1, 1) = 0.025, p(1, 2) = 0.12, p(1, 3) = 0.21 p(2, 1) = 0.18, p(2, 2) = 0.16, p(2, 3) = c. and p(x1, x2) = 0 otherwise. (a) Find the value of c. (b) Find the marginal probability mass functions of X1 and X2. (c) Are X1 and X2 independent?...

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36...

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36 for X1 = 1, 2, 3 and X2 = 1, 2, 3, find the joint probability distribution of X1*X2 and the joint probability distribution of X1/X2.

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1 0 < x2 < 1 , otherwise (ii) Calculate E(X1) and E(X2) (iii) Are the variables X1 and X2 stochastically independent? (iv) Given the variables in the question, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0 0 otherwise Find Cov(X2, X3)

Let X1, X2, . . . be iid random variables following a uniform distribution on the...

Let X1, X2, . . . be iid random variables following a uniform distribution on the interval [0, θ]. Show that max(X1, . . . , Xn) → θ in probability as n → ∞

Suppose that X1 and X2 are independent continuous random variables with the same probability density function...

Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x)= x/2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2, ). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y ).

Let X1, X2, … , X8 be a random sample of size 8 from a distribution with probability density function

Let X1, X2, … , X8 be a random sample of size 8 from a distribution with probability density function where x ≥ 1. What is the likelihood ratio critical region for testing the null hypothesis ??: ? = 1 against ?1: ? ≠ 1? If ? = 0.1, determine the best likelihood ratio critical region?

Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf f(x1, x2)...

Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) , 0<x1<1 0<x2<1 0, otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)

Let X1, X2, ..., Xn be a random sample of size from a distribution with probability...

Let X1, X2, ..., Xn be a random sample of size from a distribution with probability density function f(x) = λxλ−1 , 0 < x < 1, λ > 0 a) Get the method of moments estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3. b) Get the maximum likelihood estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3.

Consider random variables X1, X2, and X3 with binomial distribution, uniform, and normal probability density functions...

Consider random variables X1, X2, and X3 with binomial distribution, uniform, and normal probability density functions (PDF) respectively. Generate list of 50 random values, between 0 and 50, for these variables and store them with names Data1, Data2, and Data3 respectively. ( To complete successfully this homework on Stochastic Models, you need to use one of the software tools: Excel, SPSS or Mathematica, to answer the following items, and print out your results directly from the software.)

Question