Problem #1: Let X~ Unif[-2, 2], and Y = (X+ 1)².Problem #1(a):Problem #1(b):(a) Find fy() and fy(4), where fy() is the probability density function of Y.Separate your answers with a comma.(b) Find P{Y < 4}.Enter your answer symbolically,as in these examplesEnter your answer symbolically,as in these examples

If X~U(-2,2) then pdf of X, f(x)= 1/(2-(-2)) = 1/4 ; -2<x<2

Answered: Problem #1: Let X~ Unif[-2, 2], and Y =…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q3. (a) Define a function g(x) of a random [ 1; if x2X, 0; otherwise variables by g(x)% = Where x, is a real number -o< X, <∞ Show that E [g (X)] = 1-F, (x,)
1. Suppose we have a random sample X₁, X2, ..., Xn from an Exponential distribution with mean 1/A. Suppose we want to estimate the mean 1/A. One estimator for 1/X is T₁ = X. Of interest is to note that the minimum of X₁, X2,..., Xn, say X(1), has an Exponential distribution with mean (n)-¹. (a) Show that T₁ is an unbiased estimator of 1/A. (b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X. (c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?
X~Uniform [0,10]. Find Prob(X>7|X>5).
can you please expand and explainn this problem
Example 2.1.1 Let S = R, and suppose P is a probability measure on R. Define F(x) by F(x) = P((-∞, x]), XER. (2.3) Then (i) F is right continuous,
Please solve P1
Example 7-36. Let {Xx} be mutually independent, each assuming the values 0.12 . ..., a - 1 with probability . Let S, = X1 + X2 + ... + Xp. Show that the probability generatino (6) = {; P (s) : 1- sa a(1 – s) function of S, is : P (S„ = j) = £ (-1)"*j*av (4)(;=u) and hence %3D - av v=0
Suppose Z~ N(0,1) and Y = e². (a) Find the cdf Fy(a) and pdf fy(y) for Y. (For the CDF, the best you can do is write it in terms of the standard normal cdf.) (b) We don't have a formula for $(z) so we don't have a formula for quantiles. So we have to write quantiles in terms of -¹. (i) Write the 0.33 quantile of Z in terms of -1 (ii) Write the 0.9 quatntile of Y in terms of -¹. (iii) Find the median of Y.
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c = 0.95, x= 13.4, s = 3.0, n=8 I (Round to one decimal place as needed.)
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Can you solve this using "A=5, B=0"?
Question 2.1 The joint probability function of X and Y is given by f(x, y) = (1/20) * (x + 3y)for 1 < x < 3 and 0 < y < 2. Find; a. P (0 < x < 2)

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