The life (in months) of a certain computer component has a probability density function defined by f(z) = e-/3 for x in (0, 00). Find the probability that a component randomly selected will last between 12 and 18 months?

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: Topic- probability

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A: Given,

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A: Topic:- probability density function  Note:- as per our guideline if more than one question uploaded…

Q: Let sinx 0 <x<n f(x) = otherwise be probability density function of X, Compute var(x)?

A: The variance of X is defined as Var(X) = E(X2) - (E(X))2

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A: The probability density function is given as  f(x) = 4x0≤x≤124-4x12&lt;x≤10otherwise The cummulative…

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Q: What is the probability density function of W =min{X, Y }

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A: It is an important part of statistics. It is widely used.

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Q: The life (in years) of a laptop battery has a probability density function defined by…

A:

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Q: For the one that is a probability density function, find the probability that is between 0 and 0.2.

A: ∫ -∞∞f(x)=1⇒∫ -∞0f(x) + ∫0∞f(x)⇒∫ -∞00 + ∫0∞8e-8x⇒8e-8x-80∞⇒-e-∞-e0⇒-e∞≠1 this is not a pdf

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Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?

A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.

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A: Solution

Q: Then the probability density of Y = In (X) is equal %3D

A: The CDF Y is given by   ​​​​​​​

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A: given pdf function fx=115+13xand x= machine has usefull life ; 4 ≤x≤7

Q: Determine the value of c that makes the function f (x,y) = cxy for 0 < x < 4 and 0 < y < 4 satisfies…

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Q: f(x) = kx³/² 0 ≤ x ≤ 5 and 0 otherwise.

A: Solution

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!