Find k to make ?(?)=??(2−?)f(x)=kx(2−x) as a legitimate pdf(probability density function), where 0

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…

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: (this is the pdf that was validated in #4 from above). Find the probability that the number lies in…

A: Let X have the pdf is, f(x)=3x2, 0≤x≤1 To find P0≤X≤13.

Q: For the continuous distribution dF = yo (x -x) dx, 0SxS1. Find the arithmetic mean, the mode and…

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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: 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: EX : 3.1 Suppose that X, the reaction time to a stimulus, has a uniform distribution on the interval…

A: Let X1, X2, ..., Xn be  a random sample of reaction times to a stimulus following U0,θ We can…

Q: Suppose that X takes values between 0 and 1 and has probability density function x2 (2x +). If Y…

A: The arithmetic mean of squares of deviations taken from the arithmetic mean is called as…

Q: 4 Consider the following two functions, each having an unknown parameter c. f(z) = c(x² + 4x + 7) -5…

A: *answer:

Q: Let X be a random variable with probability density function 3 -x², -1 < x < 1 2 Which of the…

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Q: 2.5.12.) The length of time that an individual talks on a long-distance telephone call has been…

A: Given pdf  f(x)=ɑe-1/5x x≥0

Q: a) What must c be for the function to be a probability density function? b) Calculate F(1).

A: c can be calculated as:

Q: 5. Let X be a random variable with the PDF f(x) = r - 1| for 0 0.5) (c) Calculate E(X) and Var(X)

A: The pdf of X is

Q: The thickness of a wooden shelf in mm, has probability density function             f(x) = {0.75 –…

A: Given :  The thickness of a wooden shelf in mm, has probability density function   f(x) = {0.75 –…

Q: Consider the probability density function if x -4 + (x+4)³ Find the median. Select one:

A: Given information: fx=1x+43 if x≥-4+12 Consider, Fx=∫-4+12xftdt       =∫-4+12x1x+43dx      =-12x+42…

Q: 4 Consider the following functions: f(x) = 12x cx 0≤x≤4 4 ≤ x ≤ 6 otherwise. G(x) = 0 0.1 +0.1…

A: Given thatpdf of X f(x)= x/12.    for 0≤x≤4         4/5-cx for 4≤x≤6            0.…

Q: If X has the probability density *21 S(a) = 0 a < 1 Find P (1 < X < 5). Select one: O a.0.93 a. 0.93…

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Q: P(X = 5) = f(5) O for only continuous distributions. O for all distributions. O for some discrete…

A: From the given questions, It is given that, PrX=5=f5

Q: Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of…

A: The probability density function of X is given by,We need to find,

Q: Suppose the random variable T is the length of life of an object (possibly the lifetime of an…

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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!