Answered: Let X1 and X2 be two independent and…

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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What is the distribution of X + Y when X and Y are independent random variables with uniform distribution in (0, 1)?
The probability that data are entered incorrectly into a field in a database is 0.008. A data entry form has 24 fields, and errors occur independently for each field. The random variable X is the number of fields on the form with an error. Does X have a discrete uniform distribution? Why or why not?
Find P(X=3)
Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
Let Y be a binomial random variable with n = 10 and p = 0.3. (a) P(3 < Y < 5) = P(3 ≤ Y < 5) = (b) P(3 < Y ≤ 5) = P(3 ≤ Y ≤ 5) =
A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by Please show complete solution.
If is a random variable that has a uniform distribution on the interval [0, 10], then p(x+ 27) PX+ is equal to
Let X be a random variable with a uniform distribution over the interval (-10, 4]. Compute P(X > -1.4) [The answer should be a number rounded to five decimal places, don't use symbols such as %) Compute Fx(-0.1). [The answer should be a number rounded to five decimal places, don't use symbols such as %)
Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).
Let X and Y be independent exponential random variables with parameters 2 and 3. (a) What is the probability that X + Y > 1. (b) Conditional on X + Y = 1, what is the distribution of X.
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 56 minutes and a maximum of 100 minutes. What is the probability that a flight is less than 63 minutes?
Obtain the maximum likelihood estimate 0 of for the probability distribution.

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Let X1 and X2 be two independent and identically distributed random variables with N(µ, 1) distribution. Calculate the conditional distribution X1 | {X1 + X2 = s}.