Please answer the questions included in the image. fx,x(x, y) = (x + y²),0 t+s|X> t) = P(X > s).Hint: Find the cdf of X first, and note that P(X >t+snX > t) = P(X >t + s)Q4. Roll a fair die (uniform 1,2,3,4,5,6) repeatedly. You and Peter are betting on the number shown on each roll.If the number is 4 or less, you win $1; otherwise, you pay Peter $2.5.a) What is the expected value of the payoff for you?b) What is the variance of your payoff?Q5. Let X be uniformly distributed (continuous) on the interval [1,2]. Find E(1/X).Q6. Let us assume that the lifetime of light bulbs follows an exponential distribution with the pdf:f(x) = A exp(-Ax)We test 10 bulbs and their lifetimes are 5, 3, 5, 1, 7, 3, 4, 8, 2, 3 years, respectively. What is the MLE for X? Whatis the method of moments estimator for X?Q7. Let x,, X2, ... Xn be an iid sample with pdff(x|0) = 0xº-!,0< x < 1,0 > 0Find the MLE of 0.

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Description: Please answer the questions included in the image. fx,x(x, y) = (x + y²),0 t+s|X> t) = P(X > s).Hint: Find the cdf of X first, and note that P(X >t+snX > t) = P(X >t + s)Q4. Roll a fair die (uniform 1,2,3,4,5,6) repeatedly. You and Peter are betting

Answered: fx.v (x,y) = (x + y²), 0

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fx.v (x,y) = (x + y²), 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Topic Video

Question

Please answer the questions included in the image.

fx,x(x, y) = (x + y²),
0<x< 1,0 < y<1
a) What is the marginal pdf of fy (y)?
b) What is the conditional pdf of fx|Y (x\y = 0.5)?
%3D
Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer
service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if
you have waited an hour on the line or just picked up the phone. Formally, if X ~ exponential(), f(x) = A exp(-
Ax), and t and s are two positive numbers, use the definition of conditional probability to show that
P(X > t+s|X> t) = P(X > s).
Hint: Find the cdf of X first, and note that P(X >t+snX > t) = P(X >t + s)
Q4. Roll a fair die (uniform 1,2,3,4,5,6) repeatedly. You and Peter are betting on the number shown on each roll.
If the number is 4 or less, you win $1; otherwise, you pay Peter $2.5.
a) What is the expected value of the payoff for you?
b) What is the variance of your payoff?
Q5. Let X be uniformly distributed (continuous) on the interval [1,2]. Find E(1/X).
Q6. Let us assume that the lifetime of light bulbs follows an exponential distribution with the pdf:
f(x) = A exp(-Ax)
We test 10 bulbs and their lifetimes are 5, 3, 5, 1, 7, 3, 4, 8, 2, 3 years, respectively. What is the MLE for X? What
is the method of moments estimator for X?
Q7. Let x,, X2, ... Xn be an iid sample with pdf
f(x|0) = 0xº-!,0< x < 1,0 > 0
Find the MLE of 0.

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