6. The probability density function of the length of a hinge for fastening a door isf(x) = 1.25 for 74.6

The probability density function provides the probability at each possible value of a continuous…

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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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If X = ln Y has a normal distribution with the mean μand the standard deviation σ, find the probability densityof Y which is said to have the log-normal distribution.
2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0
According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21
Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.
1. Each rear tire on an experimental airplane is supposed to be lled to a pressure of 40 pounds per square inch (psi). Let Y1 denote the actual air pressure for the right tire and Y2 denote the actual air pressure for the left tire. Suppose that Y1 and Y2 are random variables with the joint density function attached as a photo. a) Find k. b) Find the joint distribution function for Y1 and Y2. c) Find the probability that both tires are underfilled.
2. Assume that if a certain scale in a laboratory has been used too long without recalibration the probability density function of the measurement error is f(x) = 1 – 0.5x for 0
3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
The density function of the continuous random variable X is shown below. When c≈ 0.163, Find: (1) the mode, (2) the median, and (3) the mean. Jcsin (2 -0.2x) for 1≤ x ≤ 10 f(x) = {0 elsewhere mahamdy@uoanbar.edu.iq
A density curve consists of the line segment connecting the points (0,1) and (0.5,1) and the segment connecting(0.5, 1) to the x-axis.a. Determine the coordinate point where the second segment crosses the x-axis.b. Determine the slope of that segmentc. Determine the equation of the line containing this segment (y = mx + b)d. Calculate the probability P(X > 1)
I choose a random sample of 5 of 20 sofas and I find that all of them are more than $400. If only 10 of these sofas were supposed to be more than $400, what is the probability I would get 5 costing more than $400 in my sample of 5? What would that probability be if 11 of the sofas cost more than $400? Or 12 sofas costing more than $400?
Q2. The duration of a construction activity was estimated to be in the range [2, 6] days with a most likely duration of 4 days. A construction engineer used the following symmetric density function to model the duration: fx(x) = 12 8 12 X 12' for 2 ≤x≤4 for 4 ≤x≤6 Determine the (a) mean, (b) variance, (c) standard deviation, (d) coefficient of variation, and (e) skewness.

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6. The probability density function of the length of a hinge for fastening a door is f(x) = 1.25 for 74.6