What is the MLE of g(0) ==¹? 1+0
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10.STATISTICAL INFERENCE
Question 2 c
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- Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?Suppose X and Y are independent and identically distributed (i.i.d.) randomvariables, each with the uniform distribution on [0, 1]. What is the cumulative distributionfunction and the density function of XY ?
- Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),Let the random variable Y denote the time (in minutes) for which a customer is waiting for the beginning of a service station since its arrival and let X denote the time (minutes) until the service is completed since its arrival at the service station. Since both X and Y measure the time since the arrival of the customer at the service station, always Y<X is true. The joint probability density function for X and Y is given as follows: fxy(x,y)=c(x+y) for 0<x<2 and 0<y<x what is the value of c? what is the covariance of X and Y? what is the correlation of X and Y?Let Y1 = 0.5, Y2 = 0.25, Y3 = 0.75, Y4 = 0.25 and Y5 = 1.25 be a random sample of width 5 selected from the population with the following probability density function. Which of the following is the estimation value obtained by the moment method for the unknown q parameter of this population?
- 2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for (Χ,Y ) is given by the following table: X Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance. Find the probability that a randomly selected policy holder has a home deduction of at least K100. Are the random variables Χ and Y independent? Explain your answer. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected…
- Let the continuous random variable X denote the current measured in a thin copper wire in milliamperes. Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?Suppose that Y1, . . . , Yn is a random sample from a population whose density function isSuppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?