Problem #1: Choose a point uniformly at random in the unit square (square of side length one). Let D be the distance of thepoint chosen to the nearest edge of the square.Problem #1(a):Problem #1(b):Problem #1(c):(a) Compute PD > 0.15).(b) Let fo denote the probability density function of D. Evaluate fp(0.28).(c) Calculate E[D].answer correct to 4 decimalsanswer correct to 4 decimals

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Answered: Problem #1: Choose a point uniformly at…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

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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Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the Mean
J 1 Problem 126. Let X and Y be discrete random variables with joint probability mass function pX,Y (x, y) = C/[(x + y − 1)(x + y)(x + y + 1)], x, y = 1, 2, 3, . . . Determine the marginal mass functions of X and Y
Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
Problem 1. Consider the following density function. f(x )=[ (kx) ^ (2/3) * 0 < x < 2 Find the value of k. Find the cumulative distribution function ( CDF) of X Find the inverse of the CDF. Simulate a random sample of 10000 values from the above distribution by using inversetransformation and find the mean and the variance of those values, and write the Rcode.
Question 10 The joint probability density function of X and Y is given by
Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hours
Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 9 that contain ink and 3 that do not contain ink. A sample of 6 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Find the probability density function. Be certain to list the values of Y in ascending order.
Problem 3 If the probability density function of random variable is given by f(x)=1/sech x 1 ≤ x ≤ 2 a)Find the mean b)Find the total area
Problem 45 Please Answer quickly.. In your pocket you have three dimes (coins of 10 cents) and two quarters (coins of 25 cents). You grab at random two coins from your pocket. What is the probability mass function of the amount you grabbed?
QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…
Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)

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