The snowfall in inches at a particular location is given by the following probability densityfunction:f(x):=f(x)f(x)=2x1252520I125 1250 ≤x≤55 ≤ x ≤ 1010 ≤ x ≤ 20a) Verify that the above function satisfies the property of a PDF.b) A severe snowstorm is defined as a snow storm whose snowfall is greater than or equalto 12 inches. A snowstorm is termed as disastrous if the snowfall is greater than orequal to 16 inches. If we know a particular snowstorm is severe, what is the probabilitythat the snowstorm will be disastrous?c) In a year, the location experiences three snowstorms. What is the probability that atleast one of the three snow storms is severe (assume the amount of snow falling in eachsnow storm is independent)?

Let X be a continuous random variable denoting the snowfall in inches.Given the probability density…

Answered: The snowfall in inches at a particular…

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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Which of the following functions are allowable as a probability density function for some continuous random variable? 0 A B D E F A: f₁(x) = C: f3(x) = {8² √3x² −1≤x≤0 else 10 I² x > 10 x < 10 E: f5(x) = 1- B: f₂(x) = D: f4(x) = x² −1 < x < 1 else {50 [5(1-x²)4 0≤x≤ 1 else (8x² - 6x +1) 0≤x≤1 else F: Neither
In Minecraft, about 5 zombies will spawn every minute. Define X as the waiting time in minutes for the first zombie to spawn. The probability density function is then given by f (x) = 0, x > 0 x < 0 Find the CDF, F(x). Write your answer as a piecewise function.
The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2
Find o for the following continuous distribution: f(x) = 2(1-x), 0 < x < 1.
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
1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.
For any number of x, the cumulative distribution function (F(x)) is the probability that the observed value of the X will be at most x. Select one: True False
A sample of women's heights was taken. Their heights (in inches) are defined by the following probability function. 0.0825x5.0325 for 61 < x < 65 f(x) = -0.0425x + 2.9325 0 for 65 ≤ x < 69 elsewhere The graph of f(x), the density curve, is shown below. 0.35 0.30 0.25 0.20 A 0.15 0.10 0.05 0.00 61 62 63 64 65 66 67 68 69 Height Part 1 of 3 Find the probability that a randomly selected woman from the sample has a height greater than 67 inches. (Round your answer to three decimal places.) Density
The central limit theorem says that: lima to0 P[ < æ] = ® (x)
Let X be a continuous random variable with probability density function xe-X x20 fxlx) = 0 otherwise The value of a Select one: a. can be any positive real number b. must be 1 c. can be any real number d. can be any positive integer
Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of X 20 28 40 50 58 70 probability 0.36 0.21 0.24 0.1225 0.0175 0.03 .0175 0.0025 Before I make the purchase, you would place my chance of saving $20 at 24%. Suppose you approach me after I pay for my items and ask: "Did you save any money?" If I answer "no", then you know I didn't save $20 and thus the chance of saving $20 changes from the unconditional chance 24% to the conditional chance 0%. However, if I answer "yes" my chance of saving $20 would get higher. What would be the conditional chance of saving $20 if you knew I got a discount? Mathematically, we seek: P(X = 20|X > 0 ). Even though it looks weird, it is just a conditional probability. Find it. P(X = 20|X > 0) = P(X = 20 and X > 0) / P(X > 0) = Hint: P(X = 20 and X > 0) be read off the table by identifying possible values where the event (X = 20 and X > 0) is true, don't use the multiplication rule. Do not round, express your…

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