Consider the following exponential probability density function.a. Which of the following is the formula for P(x ≤ xo)?1 P(x ≤ xo) = eTOFormula #2202 P(x ≤ xo) = 1-e3 P(x ≤ xo) = 1-e-20b. Find P(x ≤ 1) (to 4 decimals).c. Find P(x ≥ 4) (to 4 decimals).0.3679d. Find P(x ≤ 6) (to 4 decimals).0.7769e. Find P(1 ≤ x ≤ 6) (to 4 decimals),1f(x) = = ehfor 20

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Answered: Consider the following exponential…

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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For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [2,4] ..... a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is (Round to three decimal places as needed.)
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Determine the probability density function for the following cumulative distribution function. 0 x < 0 0.2x 0 < x < 4 4 < x < 9 9 ≤ x F(x) = 0.04x +0.64 1 Find the value of the probability density function at x = 3.
The following is a probability distribution function for X, with range 0, 1, 2, 3: P(X = 0) = 0.3; P(X = 1) = 0.2; P(X = 2) = 0.3; P(X = 3) = 0.2. Compute E(X). Round your answer to one decimal place.
2. Determine whether each of the following distributions are exponential family. For those that are, find a set of complete, minimum sufficient statistics. For those that are not, find a sufficient statistic. (a) Location Exponential: f(x) = e-(-0), x > 0. (b) f(x) = 0(1+x)(1+0), x > 0 (c) logN(u,02): f(x) = 1 a exp{-(log x-μ)²), x > 0. αν2πσ2 },
Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function. b. Find P(0.4≤X≤1). c. Find P(X≤0.4|X≤0.8) d. Find F(b) = P(X≤b) and sketch the graph of this function.
Question 2 The probability density function of the reliability of a piece of equipment is given by: a x)= a(162 – x²³) (x)=(a/1 16-x³ 0
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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