The total probability associated with each value of x is the corresponding row total. We found that for x = 1, the corresponding probability is f(x = 1) = 0.30. When x = 2, f(x = 2) = 0.53, and when x = 3, f(x = 3) = 0.17. Use these values to find the expectedvalue of x.E(x) = xf(x)= 1(0.30) + 2/+ 3(0.17)

X 1 2 3 Probability value (f(x)) 0.30 0.53 0.17

Answered: The total probability associated with…

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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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(λ), f(x) = λ exp(- λx), 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 + s Ç X > t) = P(X > t + s)
The variance of Y is σ2y = 4.6875 and the variance of the sum is σ2x + y = 9.1875. You knowthe variance of X=1. Find the covariance, xy. Show work
TF.8
For each of the following situations, write down the likelihood function L(θ), where θ is the probability of heads for the coin described. You toss a coin 50 times and see that it came up heads 35 times and tails 15 times. You toss a coin 100 times and see that it came up heads 54 times and tails 45 times. You don't know which way it came up the last time because it rolled into a drain was lost. You decide to toss a coin until it comes up heads the first time and then toss it 10 more times. It first comes up heads on the third toss and then comes up heads 5 more times in 10 tosses.
A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.
Suppose you are fitting a survival model and the outcome of interest is time to the diagnosis of cancer (T). A subject entered the study at t=0 and the diagnosis of cancer did not occur by the end of the study period, what kind of event is that? It is an interval-censored observation because an event happened between time of entry and the exit. It is a right-censored observation because no event will be observed during the study period. It is a left-censored observation where the event of interest happened before the study starts. It is a right-censored observation because the event has already occurred.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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