4. A random variable X with a probability density function f(x) = {xe 0 (xe-x for x > 0 else a. Find the probability that X is between 2 and 4 b Find the probability that the value of X exceeds 3

Q: x (10-x) Q1. Show that f(x): ;0<x < 10; is a probability density function. 5000

A: To be a probability density function, the sum of all f(x) must be 1. so we must…

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A:

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A: From the given Histogram first we prepare the frequency distribution table: Class Frequency…

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A: From the given information,  Pdf of the random variable X is,  fXx=c1-x2    -a≤x≤a0…

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A: The probability density function of random variable X is , f(x) =ce-xfor x ≥00otherwise

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A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: Let X be a random variable with probability density function given by x -1 0 1 f(x) a b 0.25

A: From the given information, x -1 0 1 f(x) a b 0.25 From the probability condition,…

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A: Given : x(sum of numbers on two dies)=4 , 7 N(number of rolls required)

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Q: 2 The function p₂ (x) can be used to model the service life of Product A. (i) Using definite…

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Q: 9. The density function of a random variable X is expressed as f(x) = e4-x for x > 4. Find the…

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A: Total probability of a probability density function must be 1.

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Q: Consider the probability density function f(x) = 2x if 0 <x<1 %3D The Expected Value E(x) 2/3 .a O…

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Q: (b) Find E(X). Find Var(X). otherwise.

A: Pdf of X is f(x)=132(8−x) , 0 ≤ x ≤ 8.

Q: (try) Example 41 A cortinuous random variable X has a probability density function f(x) as follows:…

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A: f(x)=e-x ; x≥0

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Q: AASAp

A: The problem can be solved using the properties of the probability density function.

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A: See the below solution

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A: The mean of the function is given by, μ=Ex=∫02xfxdx=∫02x·x2dx=12∫02x2dx=12x3302=43

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A: Probability density function is a concept is statistics.

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A: Given,f(x)=32x ; 0&lt;x&lt;1

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A: E(1Y) = ∫-∞∞1yf(y) dy

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Q: 16. For the probability density function shown, what is the probability of the random variable æ…

A: To find: The probability of the random variable x being less than 1/3 ?

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Q: (2) J ?Q13) Consider the following probability density function, what is the F(14) 0.22 X= 7 0.22…

A: We have given that the probability density function at different values of X.