A random variable X has probability density function (x² + 2x + 4) for 0 < x < 3 f(x) = otherwise. Which of the following gives the cumulative distribution function F(x)?

Q: 3. Suppose that the probability density function of X is [3x?, lo, 0 < x< 1 f(x) = otherwise…

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Q: A continuous random variable X has the probability density function 2 -(9 – x) if 0 < x < 9 81 f(x)…

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Q: Exercise 3.3 Suppose that the probability density function of X is 0 2/3). 0,

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Q: A continuous random variable X, with mean unity, has probability density function fx(x) given by (a…

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Q: -2x f(x) 0, otherwise Let X be a random variable whose probability density function is given by what…

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Q: A random variable has the following probability density function 1 -1--

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Q: The probability density function of random variable X is given as: f(x) = {4 – Bx if 0 < x < 1…

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Q: If X is the continuous random variable whose probability density function,Finc P(X=2) for 0≤x≤4 f(x)…

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Q: 1) The probability density function of X is: f(x) = 4xe-2x x>0 Calculate F(5) = ? where F indicates…

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Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: The probability density function of X is obtained below: f(x)=0.5e-0.5x;x≥0 where x is a random…

Q: 7. If the joint probability density function of X and Y is 1 if 0 < x < 1; 0 < y < 1 f(x, y)…

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Q: The probability density function for the continuous random variable X is given by: (A(x² 2x + 21)…

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Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

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

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

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Q: What should be the value of k for f(x) to be able to be a probability density function? f(x)=(2kx)/6…

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Q: A random variable has the following probability density function 1 -1--X <1 2

A: We want to find cdf and probability

Q: Two Random Variables X And Y Have The Following Joint Probability Density Function (PDF) fxx (x,y) =…

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Q: 3. Find the value of k so that f(x) for 1 < x < 2 is a probability density function. (x + 1)?

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Q: Find the cumulative distribution function for the probability density function f(x) = on the…

A: We have   Cumulative distribution function for the probability density function.

Q: If the probability density function of a continuous random variable X is [.5x 0< x<2 f(x)= otherwise…

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Q: 6. Suppose a college professor never finishes her lecture before the end of the class period, and…

A: We know that the total probability is always 1.Using that we…

Q: The probability density function for a continuous random variable X has the form, Find the…

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Q: The density function of a random variable is given as fx(x) = ae-bx x20. Find the characteristic…

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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)…

A: In particular, the cdf and pdf of X is, Since, ex is an increasing function of x and Rx = [0, 1],…

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

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Q: A random variable X has a distribution function given by: (0, F(x)= {k(x-1)*, 13 1. Determine the…

A: Probability is the chances of occurrence of an event. The probability density function f(x) gives…

Q: A continuous random variable X has the probability density function if 0 < x < 8 { (8 – x) 32 f(x) =…

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Q: The probability density function of Y = 5X + 3 is:

A: To obtain the probability density function of Y=5X+3, we will use the transformation method.

Q: Let the probability density function of the random variable x be f(x) = { e^2x  if x≤0          {…

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Q: (a) A random variable X has the following probability density function k, 0sx<1 f(x) = }x/4, 1<x<2 0…

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Q: A random variable X has a probability density function 0; x < 0, 0≤x≤1, 1<x<∞0. f(x)= { 22

A: a) Given information: fx=0, x&lt;012, 0≤x≤112x2, 1&lt;x&lt;∞

Q: 7. Let X be a continuous random variable with probability density function given by Se-(z-z0) x > x0…

A: Let X be the continuous random variable with probability density function is,  f(x) = { e^-(x-x0)…

Q: If the probability density function of a continuous random variable X is 0.50x 0x) = 0.4

A: Given,f(x)=0.5x   ;  0≤x≤20         ;  otherwise

Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

A: given that  the score of a student on a certain exam is represent by a number between 0 and 1…

Q: A continuous random variable X has the following probability density function: Jar² if-1≤x≤1 f(x) =…

A: Let x be a random continuous random variable such that (1) f(x) ≥0   for ∀ x (2) Sum of p.d.f. is 1…

Q: If f(x) = e-& ; 0 3) —

A: Given,f(x)=e-x ;0&lt;x&lt;∞

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

A: For the given pdf Find c= ?

Q: If the probability density function of the random variable X is given by 0<x<1 f(x)={x otherwise

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

A: As the graph given above in question: It is clear that fx≥0, for all x∈ℝ. So,…

Q: Example 1 Let X have the probability density function 2x ,0<x<k f(x) = {kz 0 ,e.w. For what value of…

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Q: Is 0.5e -0.5x a probability density function on the interval [0, ∞)? If so, what kind of proba-

A: The Exponential distribution is one of the continuous probability distribution and has one parameter…

Q: A continuous random variable has probability density function given by K(2x-3);1&lt;x2 Find k if…

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Q: Let X be a continuous random variable with a probability density function ((6-3e)x² + ex 0 0<x< 1…

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Q: The probability density function of a random variable is kx3 f(x) = if 0 <x< 2 V25 – x2 = 0…

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Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

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Q: suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then…

A: In question, Given X has an exponential distribution with probability density function f(x) =2e^-2x,…

Q: 3. Suppose X and Y have joint probability density function f(x,y) = {"0. 0 < x< 1,0 < y <1- x…

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Q: The probability density function of a continuous random variable is: 4 (1+x) if -1 < x < 0 x < 0) 5…

A: From the given information, fx=451+x, if -1&lt;x&lt;04153-2x, if 0≤x&lt;32   For -1&lt;x&lt;0,…

Q: (8) The moment generating function of the random variable X having the probability density function…

A: Since , the probability density function is given by ,  Our aim is to find the moment generating…

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!