please show your work Part 1. The Continuous Uniform Distribution 5. The pdf for this In...
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF
Problem 5. Let X...
6. Consider the pdf of the Uniform distribution. 5(8:2,5) = {B=A 1 A<x<B f(x; A,B) = B-A otherwise We computed the expected value in class on 11/7/2019. Find the variance of the Uniform distribution. Simplify as much as possible. Hint: B3 – A3 = (B – A)(B2 + AB + A2)
please show work and explain for my understanding.
Suppose that the continuous random variable X has pdf given by: x <1 0.16x 15 x 33 f(x)= 0.06 3<x55 [124 x>5 • Find the corresponding cdf for X: You must determine the arbitrary constants. x <1 1<x3 Ex(x)={ 3< x <5 x>5 • Use the cdf to find P(2.4 <x< 10) = • Use the cdf to determine the following percentiles: the 50th percentile (median) the 80th percentile the 90th percentile
please calculate the CDF
&PDF of the distribution.
(BP) Given X, ~ Uniform[0, 1] for i-1,.., n. What is the distribution of M:- min(X1 , ...., Xn)?
LetX1,...,Xnbe a random sample from a continuous distribution with the probability densityfunction (pdf) with an unknown parameterθ:fX(x;θ) ={0.5(x−θ)−1/2, θ < x < θ+ 1,0,otherwise.DefineYn= max{X1,...,Xn}.(a) Show thatY∗=Yn−θis a pivot, e.g., the distribution ofY∗does not depend onθ. Usethis pivot to construct a two-sided 80% confidence interval forθifn= 4 and the dataare 1.7,1.6,1.9,1.8. b.We reject the null hypothesisH0:θ= 1 in favor ofH1:θ= 1.5 ifYn> c. Assumingn= 4, find 1.5< c <2 such that the probability of type 1 error is five times...
5.2 The Uniform Distribution Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 | Table 5.4 CHAPTER 5 CONTINUOUS RANDOM VARIABLES 325 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean = 2.50 and the sample standard deviation = 0.8302....
Question 1 Solve the problem. If a continuous uniform distribution has parameters of u 0 and a 1, then the minimum 3 and the maximum is 3. For this distribution, find P(-1 < x < 0.5). Round your answer to three decimal places. IS 0.289 0.25 0.433 0.577
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Suppose that a random variable X has the following pdf. 2(1-2) 0.5 SX < 1 0 otherwise where p is simply a constant that has yet to be specified (in other words, p isa parameter). For now, we will leave the parameter p an unspecified constant Find P(X>08) Note: your answer will be an expression containing p. Suppose that k>0 is also a constant (not yet specified). Find the expected value of the random...
#5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1
#5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1
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3. The joint pdf for random variables X and Y is given by 0 otherwise (a) Determine the value of c that makes this a valid joint pdf. (b) Determine P(X<3,Y< 2). (c) What is the marginal pdf of Y?