)The cumulative distribution function of a random variable X is defined by the equation if x< 0 x² 2 1 F(x) if x>1 a. Determine the probability density function of the random variable X b. Determine the probability random variable x from ½ to 1 c. Is the probability density function a valid PDF?

Q: 1 The life (in years) of a laptop battery has a probability density function defined by P(x) = -z/3…

A: We have given that the life of a laptop battery has a pdf defined by,     P(x) = f(x) = (1/3)*e-x/3,…

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A:

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A:

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A: We have given that, Let X be a random variable that follows U(0,2).   The probability density…

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A: *Answer:

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A:

Q: If a random variable X has the probability density function Sxe-* ,x > 0 ,otherwise' f(x) = Then…

A: Given,   fx = xe-x      ; x&gt;00             ; otherwise

Q: The cumulative distribution function of a random variable X is defined by the equation if x 1…

A: The cumulative distribution function of a random variable X is defined by the equation Fx=0…

Q: Let X be a random variable whose probability density function is given by -2kx f(x) = +-e-kr x > 0…

A: Given that k=0.75 And the probability density function is, f(x)=e-2*0.75x+12e-0.75x, x&gt;0…

Q: 3. Suppose that the probability density function of x is f(x) = {°0," (3x?, 0<x < 11 0, elsewhere)…

A:

Q: Suppose that the probability density function of x is (3x², 0 (2/3)) b) Determine the cumulative…

A:

Q: The probability density function of the random variable X is given by: Sce-2x 0 f(x)= = for x > 0…

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A:

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A: Here X denotes current measured in copper wire in milliamperes. X ranges from 0 to 1/0.14. and  f(x)…

Q: Suppose that the probability density function of X is 0 2/3)

A: The given probability density function of X is fx=3x2,0&lt;x&lt;10, otherwise

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A: From the given information, f(X)=0.12, 0≤X≤10.12 Formula for Variance: V(X)=EX2-E(X)2 Consider,…

Q: Suppose that X is a random variable with the probability density function given by (2(1-x), 0≤x≤1…

A:

Q: Consider a probability density function for a random variable X, defined by for 1 < x < 3 f(x) = 16…

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Q: (a) Let X be a random variable of the continuous type with probability density function f(x). which…

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Q: Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b)…

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Q: Suppose that the probability density function of x is f(x) = 0, (3x², 0 (2/3)) b) Determine the…

A:

Q: Suppose that the random variable X has the probability density function for -1< x < 1 f(x) =| c(1-…

A: probability density function of random variable X;f(x)=c1-x2for -1≤x≤10elsewhere∵f(x) is p.d.f. then…

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A:

Q: The Weibull distribution has the following density function f(x) = (α / βα)*xα-1*e-(x/β)^α, y ≥ 0…

A: Weibull distribution: A continuous random variable Y is said to follow Weibull distribution with…

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A:

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Q: Suppose that X is a random variable with the probability density function given by - f(x) = {²01…

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Q: 10. The probability density function for a continuous random variable X has the form, find the value…

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Q: Find the cumulative distribution function of the random variable X whose probability density is…

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Q: Suppose that the random variable X has cumulative mass function given by if x 2. What is the…

A: We use the realtion of cdf and pdf to solve the qstn.

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A: The given density function is:

Q: 3. Suppose that the probability density function of x is [3x?, 0<x < 11 0, elsewhereS f(x) = a)…

A:

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Q: Let X be a random variable with the probability density function, Oe-ex 0 < X < ∞; f (x) = { 0, %3D…

A: Given that X follows exponential distribution, f(x)=θe-θx,0&lt;x&lt;∞0,otherwiseThen, the CDF of X…

Q: x, ,x > 0 f(x; A) = {a otherwise

A:

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A: Given : f(x) = 23(1-x) , -1≤x&lt;0

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!